Distribution

Problem 201

The scores of the students on a standardized test are normally distributed, with a mean of 500 and a standard deviation of 110 . What is the probability that a randomly selected student has a score between 350 and 550 ? Use the portion of the standard normal table below to help answer the question. \begin{tabular}{|c|c|} \hline $z$ & Probability \\ \hline 0.00 & 0.5000 \\ \hline 0.25 & 0.5987 \\ \hline 0.35 & 0.6368 \\ \hline 0.45 & 0.6736 \\ \hline 1.00 & 0.8413 \\ \hline 1.26 & 0.8961 \\ \hline 1.35 & 0.9115 \\ \hline 1.36 & 0.9131 \\ \hline \hline \end{tabular} $9 \%$ $24 \%$ $59 \%$

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Problem 202

Confidence interval for the population mean: Use of the $t$ distribution
A corporation that maintains a large fleet of company cars for the use of its sales staff is interested in the mean distance driven monthly per salesperson. The Español following list gives the monthly distances in miles driven by a random sample of 15 salespeople. $2346,2026,2561,2437,2244,2180,2108,2271,2382,1953,2356,2309,2391,1958,2605$ Send data to calculator Send data to Excel
Based on this sample, find a $99 \%$ confidence interval for the mean number of miles driven monthly by members of the sales staff, assuming that monthly driving distances are normally distributed. Give the lower limit and upper limit of the $99 \%$ confidence interval.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)
Lower limit: $\square$ Upper limit: $\square$

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Problem 203

Risk taking is an important part of investing. In order to make suitable investment decisions on behalf of their customers, portfolio managers give a questionnaire to new customers to measure their desire to take financial risks. The scores on the questionnaire are approximately normally distributed with a mean of 51 and a standard deviation of 16 . The customers with scores in the bottom $15 \%$ are described as "risk averse." What is the questionnaire score that separates customers who are considered risk averse from those who are not? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place. $\square$

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Problem 204

In a survey of 2084 adults in a recent year, 750 made a New Year's resolution to eat healthier. Construct $90 \%$ and $95 \%$ confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.
The $90 \%$ confidence interval for the population proportion $p$ is ( $0.343,0.377$ ). (Round to three decimal places as needed.) The 95\% confidence interval for the population proportion p is ( $0.339,0.381$ ). (Round to three decimal places as needed.) With the given confidence, it can be said that the $\square$ of adults who say they have made a New Year's resolution to eat healthier is $\square$ Iof the given confidence interval.

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Problem 205

Question \#2 (pg. 183) Compute the mean and variance of the following discrete probability distribution. \begin{tabular}{|cc|} \hline $\mathbf{X}$ & $\mathbf{P}(\mathbf{x})$ \\ \hline 2 & .5 \\ 8 & .3 \\ 10 & .2 \\ \hline \end{tabular}

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Problem 206

Use the Standard Normal Table or technology to find the $z$ -score that corresponds to the following cumulative area. $0.9006$
The cumulative area corresponds to the z-score of $\square$ (Round to three decimal places as needed.)

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Problem 207

Use the standard normal table to find the z-score that corresponds to the given percentile. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores. If convenient, use technology to find the z-score. $P_{15}$
Click to view page 1 of the table. Click to view page 2 of the table.
The $z$ -score that corresponds to $\mathrm{P}_{15}$ is $\square$ (Round to two decimal places as needed.)

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Problem 208

Find the z-score that has $10.2 \%$ of the distribution's area to its left.
The z-score is $\square$ (Round to two decimal places as needed.)

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Problem 209

Find the z-score that has $3.533 \%$ of the distribution's area to its left.
The z-score is $\square$ (Round to two decimal places as needed.)

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Problem 210

The pregnancy durations (in days) for a population of new mothers can be approximated by a normal distribution, with a mean of 272 days and a standard deviation of 9 days. (a) What is the minimum pregnancy durations that can be in the top $8 \%$ of pregnancy durations? (b) What pregnancy durations would be considered unusual?

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Problem 211

Question 1, 12.2.1 HW Score: $0 \%, 0$ of 6 points Points: 0 of 1 Save
Fill in the blank with an appropriate word or phrase. A listing of observed values and the corresponding frequency of occurrence of each value is called a $\qquad$ distribution.
A listing of observed values and the corresponding frequency of occurrence of each value is called a distribution. $\square$

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Problem 212

Points: 0 of 1 Save
The accompanying data represent the approximate population, in millions, of the 20 most populous cities in the world. \begin{tabular}{|c|c|c|c|c|} \hline 13.7 & 12.6 & 10.2 & 8.5 & 7.3 \\ \hline 13.5 & 11.5 & 9.6 & 8.2 & 6.9 \\ \hline 12.9 & 11.2 & 9.5 & 7.7 & 6.9 \\ \hline 12.8 & 10.4 & 8.7 & 7.7 & 6.8 \\ \hline \end{tabular}
Use these data to construct a frequency distribution with a first class of $6.5-7.5$ . Fill in the missing classes and the frequency for each class below. \begin{tabular}{c|c} \begin{tabular}{c} Population \\ (millions of people) \end{tabular} & Number of Cities \\ \hline $6.5-7.5$ & $\square$ \\ $\square-\square$ & $\square$ \\ $\square-\square$ & $\square$ \\ $9.8-10.8$ & $\square$ \\ $10.9-11.9$ & $\square$ \\ $\square-\square$ & $\square$ \\ $\square-\square$ & $\overline{20}$ \end{tabular}

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Problem 213

Suppose scores on the SAT exam are normally distributed with mean 1100 and standard deviation 200. Answer the following. (a) Aaron scored 1060 on the SAT. What proportion of students performed worse than Aaron? Round to 4 decimal places. (b) Betty scored 1199 on the SAT. What proportion of students performed better than Betty? Round to 4 decimal places. $\square$ (c) What proportion of students got a score between Aaron's and Betty's scores? Round to 4 decimal places. $\square$

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Problem 214

According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 67 inches and a standard deviation of 2.3 inches. Suppose one Martian adult male is randomly chosen. Let $X=$ height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X ? $\mathrm{X} \sim \mathrm{N}($ , $\square$ $\square$ b. Find the probability that the person is between 63.2 and 65.3 inches. $\square$ c. The middle $40 \%$ of Martian heights lie between what two numbers?
Low: $\square$ inches
High: $\square$ inches

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Problem 215

3. 21. Supozojmë se $X$ ka densitet $f(x)=e^{-x}, \quad x>0$ (a) Llogaritni funksionin prodhues të momenteve të $X$ dhe gjeni pritjen matematike, mesataren dhe dispersionin. (b) Gjeni pritjen matematike drejtpërsëdrejti nga përkufizimi.

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Problem 216

22. An instructor has given a short quiz consisting of two parts. For a randomly selected student, let $X=$ the number of points eamed on the first part and $Y=$ the number of points eamed on the second part. Suppose that the joint pmf of $X$ and $Y$ is given in the accompanying table. \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{2}{|l|}{\multirow[b]{2}{*}{ $p(x, y)$ }} & \multicolumn{4}{|c|}{ $y$ } \\ \hline & & 0 & 5 & 10 & 15 \\ \hline & 0 & . 02 & . 06 & . 02 & . 10 \\ \hline $x$ & 5 & . 04 & . 15 & . 20 & . 10 \\ \hline & 10 & .01 & .15 & . 14 & . 01 \\ \hline \end{tabular} a. If the score recorded in the grade book is the total number of points earned on the two parts, what is the expected recorded score $E(X+Y)$ ? b. If the maximum of the two scores is recorded, what is the expected recorded score?

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Problem 217

27. Annie and Alvie have agreed to meet for lunch between noon (0:00 P.M.) and 1:00 P.M. Denote Annie's arrival time by $X$ . Alvie's by $Y$ , and suppose $X$ and $Y$ are independent with pdf's $\begin{array}{l} f_{X}(x)=\left\{\begin{array}{cl} 3 x^{2} & 0 \leq x \leq 1 \\ 0 & \text { otherwise } \end{array}\right. \\ f_{X}(y)=\left\{\begin{array}{rl} 2 y & 0 \leq y \leq 1 \\ 0 & \text { otherwise } \end{array}\right. \end{array}$
What is the expected amount of time that the one who arrives first must wait for the other person? [Hint: $\quad h(X, Y)=|X-Y|$ .

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Problem 218

Weight loss: In a study to determine whether counseling could help people lose weight, a sample of people experienced a group-based behavioral intervention, which involved weekly meetings with a trained interventionist for a period of six months. The following data are the numbers of pounds lost for 14 people. Assume the population is approximately normal. Perform a hypothesis test to determine whether the mean weight loss is greater than 14 pounds. Use the $\alpha=0.10$ level of significance and the $P$ -value method with the TI-84 Plus calculator. \begin{tabular}{ccccccc} \hline 19.6 & 25.8 & 4.9 & 21.0 & 18 & 9.6 & 14.4 \\ 18.0 & 34.7 & 30.6 & 9.4 & 32.5 & 20.8 & 16.4 \\ \hline \end{tabular} Send data to Excel
Part: $0 / 5$
Part 1 of 5 (a) State the appropriate null and alternate hypotheses. $\begin{array}{l} H_{0}: \square \\ H_{1}: \square \end{array}$
This hypothesis test is a (Choose one) $\boldsymbol{\nabla}$ test. $\square$

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Problem 219

Keep cool: Following are prices, in dollars, of a random sample of ten 7.5-cubic-foot refrigerators. A consumer organization reports that the mean price of 7.5 -cubic-foot refrigerators is less than $\$ 370$ . Do the data provide convincing evidence of this claim? Use the $\alpha=0.01$ level of significance and the $P$ -method with the
Critical Values for the Student's t Distribution Table. \begin{tabular}{lllll} \hline 350 & 414 & 360 & 313 & 353 \\ 318 & 369 & 383 & 329 & 339 \\ \hline \end{tabular} Send data to Excel
Part 1 of 6
Following is a dotplot for these data. Is it reasonable to assume that the conditions for performing a hypothesis test are satisfied? Explain.
The dotplot shows that there are no $\quad$ outliers. The dotplot shows that there is no evidence of strong skewness.
We $\square$ can assume that the population is approximately normal.
It $\square$ is reasonable to assume that the conditions are satisfied.
Part: $1 / 6$
Part 2 of 6
State the appropriate null and alternate hypotheses. $H_{0}$ : $\square$ $\square$ < $\square$ $\square$ $\square$ $\square$ $\square$ $H_{1}$ : $\square$ 묵 $\square$ $\mu$

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Problem 220

Consider a Bernoulli scheme of 4000 trials, with the probability of success in a single trial equal to $1 / 4$ . Then
a. The probability that at least 2001 trials will end in success is the same as the probability that at most 1999 trials will end in success.
b. The most probable number of sucesses in this experiment amounts to 1000 c. The probability of not obtaining any successes can be approximated using the Poisson theorem with an appropriate expression for $\lambda=4000 / 4$ , and this will be a good approximation. d. Probability of not getting any successes amounts to (3/4)^4000

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Problem 221

Word problem involing calculations from a normal distribution 0.5 Natasha
A ride-sharing company has computed its mean fare to be $\$ 33.00$ , with a standard deviation of $\$ 5.20$ . Suppose that the fares are normally distributed. Español
Complete the following statements. (a) Approximately $\square$ of the company's rides have fares between $\$ 17.40$ and $\$ 48.60$ . (b) Approximately $68 \%$ of the company's rides have fares between $\$$ $\square$ and \\square$ .

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Problem 222

The table shows the distribution, by age, of a random sample of 3910 Age Distribution of Moviegoers moviegoers ages 12-74. If one moviegoer is randomly selected from this population, find the probability, expressed as a simplified fraction, that the moviegoer is not in the 65-74 age range. \begin{tabular}{|c|c|} \hline Ages & Number \\ \hline $12-24$ & 1330 \\ \hline $25-44$ & 1080 \\ \hline $45-64$ & 990 \\ \hline $65-74$ & 510 \\ \hline \end{tabular}
The probability is $\square$ (Type an integer or a simplified fraction.)

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Problem 223

On the basis of his sale records, a salesman knows that his weekly commissions have the probabilities shown below. \begin{tabular}{|l|c|c|c|c|c|} \hline Commission & 0 & $\$ 1,000$ & $\$ 2,000$ & $\$ 3,000$ & $\$ 4,000$ \\ \hline Probability & 0.11 & 0.2 & 0.49 & 0.1 & 0.1 \\ \hline \end{tabular}
Find the salesman's expected commission. \\square$

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Problem 224

Withdrawal symptoms may occur when a person using a painkiller stops using it. For a certain, widely taken painkiller, withdrawal symptoms occur in $16 \%$ of people who have stopped using the painkiller. Suppose that we will take a random sample of 10 people who have stopped using the painkiller. Let $\widehat{p}$ represent the proportion of people from the sample who experienced withdrawal symptoms. Consider the sampling distribution of the sample proportion $\hat{p}$ . Complete the following. Carry your intermediate computations to four or more decimal places. Write your answers with two decimal places, rounding if needed. (a) Find $\mu_{p}$ (the mean of the sampling distribution of the sample proportion). $\mu_{\hat{p}}=\square$ (b) Find $\sigma_{\hat{p}}$ (the standard deviation of the sampling distribution of the sample proportion). $\square$ $\sigma_{\hat{p}}=\amalg$

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Problem 225

Suppose the birth weights of full-term babies are normally distributed with mean 3250 grams and standard deviation $\sigma=480$ grams. Complete parts (a) through (c) below. (4) n 17 (c) Suppose the area under the normal curve to the riaht of $X=4210$ is 0.0228 . Provide an interpretation of this result. Select the correct choice below and fill in the answer box to complete your choice. (Type a whole number.) A. The probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is less than $\square$ grams. B. The probability is 00228 that the birth weight of a randomly chosen full-term baby in this population is more than $\square$ grams. solve this View an example Get more help - Clear all Check answer

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Problem 226

SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300 . An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the $85 \%$ confidence interval to 5 points, how many students should the administrator sample? Make sure to give a whole number answer.

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Problem 227

For the proprablility distribution table below: \begin{tabular}{|c|c|c|c|c|} \hline $x$ & $P(x)$ & $x^{2}$ & $x P(x)$ & $x^{2} P(x)$ \\ \hline 0 & 0.07 & $\square$ & $\square$ & $\square$ \\ \hline 1 & 0.22 & $\square$ & $\square$ & $\square$ \\ \hline 2 & 0.17 & $\square$ & $\square$ & $\square$ \\ \hline 3 & 0.1 & $\square$ & $\square$ & $\square$ \\ \hline 4 & 0.44 & $\square$ & & $\square$ \\ \hline \end{tabular}
Find the mean. Round to two decimal places. $\mu=$ $\square$ Find the standard deviation. Round to three decimal places. $\sigma=$ $\square$ Submit Question

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Problem 228

Switch to
You have 2 attempts to take this quiz (highest score will be taken). (3) Question 6 Community Panopto Video
You will not be able to see correct/incorrect answers between quiz attempts. (3) Question 7 Canvas Library Research Help You might not get the exact same quiz for both attempts, but they will be similar. (?) Question 8 Time Elapsed: Hide Time Attempt due: Nov 17 at 11:59pm 3 Minutes, 20 Seconds
From a sample of 16 students in our class, the mean resting heart rate was 68 bpm with a standard deviation of 12 bpm . Assuming a normal distribution, use the erripirical rule to calculate the following. What is the $95 \%$ confidence interval for the average heart rate of all students in our class? $(66,70)$ $(60,72)$ $(62,74)$ $(58,76)$ Question 2 1 pts Accessibility Resources
For a group of normally distributed scores with a mean of 200 and a standard deviation of 10,

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Problem 229

Researchers measure the heart rate from 100 students after taking a Human Physiology exam, and find a mean of 120 beats per minute (bpm), with a standard deviation of 20 bpm . Assuming a normal distribution, the middle $95 \%$ of the scores will be between: $(100,140) \mathrm{bpm}$ $(110,130)$ bpm $(80,160)$ bpm $(114,124) \mathrm{bpm}$ $(118,122) \mathrm{bpm}$

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Problem 230

According to a poll, 651 out of 1026 randomly selected smokers polled believed they are discriminated against in public life or in employment because of their smoking. a. What percentage of the smokers polled believed they are discriminated against because of their smoking? b. Check the conditions to determine whether the CLT can be used to find a confidence interval. c. Find a $95 \%$ confidence interval for the population proportion of smokers who believe they are discriminated against because of their smoking. d. Can this confidence interval be used to conclude that the majority of smokers believe they are discriminated against because of their smoking? Why or why not? a. The percentage of those taking the poll believed they are discriminated against because of their smoking is $\square$ \%. (Round to one decimal place as needed.)

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Problem 231

A poll in 2017 reported that 697 out of 1034 adults in a certain country believe that marijuana should be legalized. When this poll about the same subject was first conducted in 1969 , only $12 \%$ of the adults of the country supported legalization. Assume the conditions for using the CLT are met. Complete parts (a) through (d) below. a. Find and interpret a $99 \%$ confidence interval for the proportion of adults in the country in 2017 that believe marijuana should be legalized.
The 99\% confidence interval for the proportion of adults in the country in 2017 that believe marijuana should be legalized is ( $\square$ , (Round to three decimal places as needed.)

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Problem 232

A community college is planning to expand its library. Forty students were asked how many times they visited the library during the previous semester. Their responses are given below. Construct a frequency distribution, letting each class have a width of 1. \begin{tabular}{cccccccc} 0 & 2 & 3 & 4 & 5 & 5 & 8 & 9 \\ 0 & 2 & 3 & 4 & 5 & 5 & 8 & 9 \\ 1 & 2 & 3 & 5 & 5 & 6 & 8 & 9 \\ 1 & 2 & 3 & 5 & 5 & 7 & 8 & 10 \\ 1 & 2 & 3 & 5 & 5 & 8 & 9 & 10 \end{tabular} \begin{tabular}{|c|c|} \hline Number of Visits & Number of Students \\ \hline 0 & 2 \\ 1 & 3 \\ 2 & 5 \\ 3 & 5 \\ 4 & 2 \\ 5 & $\square$ \\ \hline \end{tabular}

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Problem 233

to conclude that the fund has moderate risk return for a certain fund. The standard deviation of the rate of return is computed to be $3.98 \%$ . Is there suffic distributed.
What are the correct hypotheses for this test? The null hypothesis is $\mathrm{H}_{0}: \sigma=0.06$ . The alternative hypothesis is $\mathrm{H}_{1}: \sigma<0.06$ . Calculate the value of the test statistic. $\chi^{2}=11.880$ (Round to three decimal places as needed.) Use technology to determine the P-value for the test statistic. The $P$ -value is $\square$ $\square$ . (Round to three decimal places as needed.) Clear all

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Problem 234

Weights of animals which are modeled by $\mathrm{N}(420 \mathrm{lbs}, 50 \mathrm{lbs}$ .)
6. There is a $94.52 \%$ chance of having the same weight as Jerry the Giraffe. How many standard deviations from the mean is he? a. 1.60 standard deviations b. 1.65 standard deviations light green c. 2.00 standard deviations black d. -1.50 standard deviations yellow grey
7. How much does Jerry weigh? a. 502 lbs purple b. 500 lbs dark red c. 520 lbs dark green d. 345 lbs light brown

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Problem 235

Midterm Exam: Ch $1(1,2) 2(1,2,3) 3(1,2,3) 4(1,2) 5(1,2,3) 6(1,2)$ Question 27 of 30 (1 point) I Question Attempt: 1 of 1 Home - Northern Ess... A Content Ivica Zubac /// Stats/... $<13$ $\equiv 14$ $=15$ 16 $=17$ 18 19 $=20$ 21 22 $=23$ Jonath: Time Remaining: 57:32
Pain: The General Social Survey asked 835 people how many days they would wait to seek medical treatment if they were suffering pain that interfered with their ability to work. The results are presented in the following table. \begin{tabular}{cc} Number of Days & Frequency \\ \hline 0 & 26 \\ 1 & 432 \\ 2 & 266 \\ 3 & 79 \\ 4 & 18 \\ 5 & 14 \\ \hline Total & 835 \end{tabular}
Part: $0 / 2$ $\square$
Part 1 of 2 (a) Compute the mean $\mu_{X}$ . Round the answer to three decimal places as needed. $\mu_{X}=\square$ $\square$

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Problem 236

h Jay I Wh. Untitied document -.. Time Remaining: 53:18 Miaterm Exam: Ch $1(1,2) 2(1,2,3) 3(1,2,3) 4(1,2) 5(1,2,3) 6(1,2)$ Question 28 of 30 (1 point) I Question Attempts 1 of 1 19 $=20$ $\equiv 21$ $\equiv 22$ 23 $=24$ $=26$ $\equiv 27$ $\equiv 28$ 29
Take a guess: A student takes a multiple-choice test that has 11 questions. Each question has five choices. The student guesses randomly at each answer. Let $X$ be the number of questions answered correctly. Round the answers to at least four decimal places.
Part: $0 / 2$
Part 1 of 2 (a) $P(6)=0.0097$
Part: $1 / 2$
Part 2 of 2 (b) $P($ More than 3 $)=$ $\square$

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Problem 237

Untitied document -- Traditional| Stats I N ... Defense | Stats | NBA.... Utah vs LA Stats \& P... Ivica Zubac III Stats /... Home - Northern Ess... Midterm Exam: Ch $1(1,2) 2(1,2,3) 3(1,2,3) 4(1,2) 5(1,2,3) 6(1,2)$ Question 30 of $30(1$ point) I Question Attempt: 1 of 1 Midterm Exam: Ch $1(1,2) 2(1,2,3) 3(1,2,3) 4(1,2) 5(1,2,2),(1,21$ Question 30 of 30 (1 point) I Question Attempt: 1 of 1 Time Remaining: $51: 21$ Jonathan lay I Wh. 三 19 $=20$ ； 21 $\equiv 22$ 23 $\equiv 24$ $=25$ $=26$ $\equiv 28$ $\equiv 29$ Españ 30
Put some air in your tires: Let $X$ represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of $X$ is as follows. \begin{tabular}{c|ccccc} $\boldsymbol{x}$ & 0 & 1 & 2 & 3 & 4 \\ \hline $\boldsymbol{P}(\boldsymbol{x})$ & 0.1 & 0.3 & 0.3 & 0.2 & 0.1 \end{tabular}.
Part: $0 / 2$
Part 1 of 2 (a) Compute the mean $\mu_{X}$ . Round the answer to three decimal places as needed. $\mu_{X}=$ $\square$

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Problem 238

ww-awualeks.com Win say 1 Wh Untitied document -- Traditional|Stats IN. Defonse I Stats INBA... Utah vs LA Stats \& P... Home - Northern Ess... Content (4) Kaicenat - Midterm Exam: Ch $(4,2) 2(1,2,3) 3(1,2,3) 4(1,2) 5(1,2,3) \operatorname{C(1,24}$ Cuestion 30 of 30 (1 point) I Question Attempt 1 of 1 Time Remaining: $50: 29$ Jonathan Español $=30$ < 19 20 21 22 23 F 25 $=26$ $\equiv 27$ $\equiv 28$ $\equiv 29$ $=30$
Put some air in your tires: Let $X$ represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of $X$ is as follows. \begin{tabular}{c|ccccc} $\boldsymbol{x}$ & 0 & 1 & 2 & 3 & 4 \\ \hline $\boldsymbol{P}(\boldsymbol{x})$ & 0.1 & 0.3 & 0.3 & 0.2 & 0.1 \end{tabular}
Part: $0 / 2$
Part 1 of 2 (a) Compute the mean $\mu_{X}$ . Round the answer to three decimal places as needed. $\mu_{X}=$ $\square$
Part: $1 / 2$
Part 2 of 2 (b) Compute the standard deviation $\sigma_{X}$ . Round the answer to three decimal places as needed. $\sigma_{X}=\square$

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Problem 239

Wait time at the DMV has an average of 37 minutes with a standard deviation of 8 minutes.
8. What is the z score for 20 minutes? a. 2.13 yellow b. -2.13 white c. 2.12 orange d. -2.12 grey
9. What is the z -score for 60 minutes? a. 2.88 dark green b. -2.88 blue c. 2.87 light brown d. -2.87 yellow
10. What is the probability of waiting less than 20 minutes? a. $98.34 \%$ purple b. $98.30 \%$ pink c. $1.66 \%$ black d. $1.70 \%$ red
11. What is the probability of waiting less than 60 minutes? a. $99.80 \%$ dark brown b. $99.79 \%$ orange c. $00.20 \%$ pink d. $00.21 \%$ blue
12. What is the probability of waiting between 20 and 60 minutes? a. $98.14 \%$ blue

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Problem 240

6 5/5 points Let $X_{1}, X_{2}, \ldots, X_{n}$ be independent and identically distributed random variables from a uniform distribution on the interval $(0, a)$ . The value of a is unknown. Derive the method of moments estimate of the parameter a. $2\left(X_{1}+\ldots+X_{n}\right) / n$ 2* median( $\mathrm{X} 1, \ldots, \mathrm{Xn}$ ) $\operatorname{Max}\left(X_{1}, X_{2}, \ldots, X_{n}\right)$

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Problem 241

The starting salaries of new graduates in a particular field are normally distributed with a mean of \ $52,000 and a standard deviation of \$4,500. a) What percentage of graduates earn between$ \ $47,500$ and $\$ 56,500$ ? b) What is the cutoff salary for the top 10\% of earners? c) If a company hires 50 graduates, how many would you expect to have starting salaries below $\$ 45,000$ ?

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Problem 242

Each year on Halloween, each child in Carrboro will visit an average of 52 houses with a standard deviation of 6 houses. The distribution of number of houses visited is approximately Normally distributed. (For \#s 1-5.)
1. What is the probability that a child will visit fewer than 47 houses this year?
2. What is the probability that they will visit more than 60 houses?
3. What percentage of children will visit between 45 and 62 houses?
4. What is the $80^{\text {th }}$ percentile of houses visited?
5. What number of houses does a child visit to be in the lowest $15 \%$ of trick-or-treaters?
6. Asher lives in Chapel Hill where the mean number of houses is 43 . He visits 50 houses which puts him in the $85^{\text {th }}$ percentile. What is the standard deviation?
7. Phin lives in Hillsborough. He visits 36 houses which is more than $32 \%$ of children in Hillsborough. The standard deviation is 7 houses. What is the mean?

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Problem 243

The probability mass function of a random variable $X$ is given by $p(i)=\frac{c \lambda^{i}}{i!}, \mathrm{i}=0,1,2, \ldots$ , where $\lambda$ is som positive value. Find ia) $P\{X=0\}$ and (b) $P\{X>2\}$ .

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Problem 244

Find the median for the data items in the given frequency distribution. \begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline Score, $\mathbf{x}$ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline Frequency, $\mathbf{f}$ & 3 & 4 & 2 & 6 & 1 & 1 & 1 & 2 \\ \hline \end{tabular}
The median is $\square$ . (Type an integer or a decimal.)

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Problem 245

A survey reported that $66 \%$ of graduating high school students enroll in college. Consider a classroom with 30 graduating high school students. What is the probability that 25 or MORE students are expected to enroll in college? $\qquad$ Note: Enter XXX.XX AT LEAST ONE DIGIT BEFORE THE DECIMAL, TWO AFTER and round up AFTER all calculations. Thus, 7 is entered as 7.00; 3.562 is entered as $\square$ A

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Problem 246

\text{Refer to Exercise 39. Define event } A : \text{ sum is 5. Find } P(A). \text{ (The scenario involves rolling 2 four-sided dice.)}

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Problem 247

Refer to the accompanying data display that results from a simple random sample of times (minutes) between eruptions of the Old Faithful geyser. The confidence level of $95 \%$ was used. Complete parts (a) through (d) below.
TInterval $\begin{array}{l} (85.74,91.76) \\ x=88.75 \\ S x=8.897431411 \\ n=36 \end{array}$ a. What are the requirements for using the methods for the mean to construct a confidence interval estimate of a population mean? A. The sample is a simple random sample and the population is normally distributed or $n \leq 30$ . B. The sample is a simple random sample, the population is normally distributed, and $n>30$ . C. The sample is a simple random sample, the population is normally distributed, and $n \leq 30$ . D. The sample is a simple random sample and the population is normally distributed or $n>30$ . b. What does it mean to say that the confidence interval methods for the mean are robust against departures from normality? A. The methods do not work well with distributions that are not normal. have only one mode, and should not include outliers. C. The methods only work with distributions that are not normal. should include outliers.

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Problem 248

السؤال الثاني:
أوجد :
1. المدى ؟
2. التباين ؟
3. الانحراف المعياري ؟

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Problem 249

Complete the probability distribution table below and then answer the questions. \begin{tabular}{|c|c|c|c|c|c|} \hline Item & Burrito & \multicolumn{2}{|c|}{ Taco } & Salad & \begin{tabular}{c} Burrito and \\ Taco \end{tabular} \\ \hline Taco and Salad \\ \hline Probability & .18 & 23 & .10 & .38 & 11 \\ \hline \end{tabular} - What is the probability a taco is NOT purchased?

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Problem 250

3. ( 0.1 puntos) Sse estima que el tiempo en horas de trabajo autónomo que se necesita para preparar y estudiar el temario de Técnicas de Investigación sigue una ley normal de media 40 horas y variancia 9 horas ${ }^{2}$ . La probabilidad de que los alumnos dediquen menos de 45 horas es 0.952 ¿Cuál es la probabilidad que una persona seleccionada al azar dedique un tiempo de trabajo autónomo entre 35 y 45 horas?

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Problem 251

(11) Situatë reale / Zgjidh problemën Tabela tregon shpërndarjen e moshave të mësuesve sipas gjinisë, meshkuj dhe femra. a Vizato shumëkëndëshin e shpërndarjes për këto dy bashkësi të dhënash në të njëjtin diagram. b Gjej mesataren e secilës nga bashkësitë e të dhënave dhe me anë të tyre krahaso shpërndarjet e moshave të mësuesve meshkuj dhe femra. c Cila karakteristikë e diagramit tënd konfirmon se krahasimi që ke bërë është i saktë? \begin{tabular}{|c|c|c|} \hline Mosha $(x$ vite $)$ & Mashkull & Femër \\ \hline $20 \leqslant x<25$ & -1 & 0 \\ \hline $25 \leqslant x<30$ & -2 & 9 \\ \hline $30 \leqslant x<35$ & 3 & 10 \\ \hline $35 \leqslant x<40$ & 7 & 12 \\ \hline $40 \leqslant x<45$ & 10 & 8 \\ \hline $45 \leqslant x<50$ & 10 & 7 \\ \hline $50 \leqslant x<55$ & 12 & 4 \\ \hline $55 \leqslant x<60$ & 4 & 0 \\ \hline $60 \leqslant x<65$ & 1 & 0 \\ \hline \end{tabular}

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Problem 252

The lifespan of some macaws in captivity is normally distributed. Their lifespan has a mean of 50 years and a standard deviation of 8 years.
What is the probability of a macaw with a lifespan greater than 60 years?

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Problem 253

44.5. Provide two recommendations for decreasing the margin of error of the interval.
Select the two recommendations that would decrease the margin of error of the interval. A. Decrease the standard deviation of hours worked. B. Decrease the confidence level. C. Increase the confidence level. D. Decrease the sample size E. Increase the sample size F. Use fewer degrees of freedom.

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Problem 254

Here is the five-number summary for the distribution of a cigarette tax (in cents) for all the states in a certain country Use this information to answer parts a through d. $\text { Minimum }=8, \text { Q1 }=37, \text { Median }=52, \text { Q3 }=97, \text { Maximum }=163$ a. About what proportion of the states have cigarette taxes (i) greater than 37 cents and (ii) greater than 97 cents? (i) About $\square$ $\%$ of the states have cigarette taxes greater than 37 cents

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Problem 255

taking 200 SRSs of 100 students from a population in which the true proportion who recycle is 0.50 . (a) Explain why the sample result does not give convincing evidence that more than half of the school's students recycle. (b) Suppose instead that 63 students in the class's sample had said "Yes." Explain why this result would give strong evidence that a majority of the school's students recycle.

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Problem 256

A preparation SAT test score can be assumed normally distributed with a historical mean of 518 and known standard deviation 114. In a training program, 50 students had an average score of 550 on the preparatory test. Test whether there has been improvement over the historical average. Use a $5 \%$ significance level. 1 What is the Table A2 CRITICAL VALUE for the problem? Note Answer Input Format for Critical Values.
Note: Enter X.XX AT LEAST ONE DIGIT BEFORE THE DECIMAL, TWO AFTER and round up. Thus, 1.645 is entered as $1.65,-2.326$ is entered as $-2.33,2.054$ is entered as $2.05,-1.282$ is entered as -1.28

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Problem 257

I
A preparation SAT test score can be assumed normally distributed with a historical mean of 518 and known standard deviation 114. In a training program, 50 students had an average score of 550 on the preparatory test. Test whether there has been improvement over the historical average. Use a $5 \%$ significance level.
1 What is the P-VALUE from Table A2 for testing HO? See two entry formats below.
Note: Two formats possible: 1) Enter LT01 if P-value is less than 0.01 2) Enter XXX.XX AT LEAST ONE DIGIT BEFORE THE DECIMAL, TWO AFTER and round up. Thus, 134.784 is entered as $134.78,35.295$ is entered as $35.30, .2749$ is entered as $0.27,-.5650$ is entered as -0.57

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Problem 258

A preparation SAT test score can be assumed normally distributed with a historical mean of 518 and known standard deviation 114. In a training program, 50 students had an average score of 550 on the preparatory test. Test whether there has been improvement over the historical average.
1 What is the CONCLUSION for HO , assuming a $1 \%$ significance level? REJ = Reject H0, assume H 1 true. FTR = Fail to Reject H0, assume HO true. CBD = Cannot be Determined.
Note: Enter REJ, FTR or CBD letters.

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Problem 259

A study time survey is conducted of 39 UGA students and a mean x-bar 110 minutes is obtained. Test whether the UGA study times differ from the national average of 120 min ? Assume study times have a normal distribution with a known standard deviation of $\sigma=30$ minutes. Use the $5 \%$ significance level.
1 What is the correct interpretation of the hypothesis testing result at the $5 \%$ level of significance? 1) = The UGA study times were greater than the national average. 2) = The UGA study times are different from the national average. 3) = There was no difference between the UGA and national study times.
Note: Enter integer 1, 2, 3 No decimal. $A$

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Problem 260

An EPA standard requires lead in lake water to be LESS than 4 ppb (parts/billion). A studied lake had 11 samples with a mean of 2.8 ppb and sample standard deviation of 1.9 ppb . The concentration of lead can be assumed normally distributed. Is the lake concentration of lead LESS than the EPA standard? Use 5\% significance level.
1 What is the Table A3 CRITICAL VALUE for the problem? Note Answer Input Format Below.
Note: Enter XXX.XX AT LEAST ONE DIGIT BEFORE THE DECIMAL, TWO AFTER and round up. Thus, 134.784 is entered as $134.78,35.295$ is entered as $35.30, .2749$ is entered as $0.27,-.5650$ is entered as -0.57 $\square$ A

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Problem 261

2. Continue to love Gaussian: $X$ and $Y$ are independent identically distributed (i.i.d.) Gaussian, i.e., $X \sim N\left(\mu, \sigma^{2}\right)$ , $Y \sim N\left(\mu, \sigma^{2}\right)$ . (a) ( $\mathbf{5} \mathbf{p t s}$ ) Define $Z=\sqrt{2} X+\sqrt{3} Y$ , find $f_{Z}(z)$ . (b) ( $\mathbf{1 0} \mathbf{~ p t s )}$ Set $\mu=0, \sigma^{2}=1$ . Find $P(\sqrt{5} \leq Z \leq 5)$ . Leave your answer in terms of $Q(\cdot)$ function.
Recall: $Q(x)=\int_{x}^{\infty} \frac{1}{\sqrt{2 \pi}} e^{-\frac{t^{2}}{2}} d t$ . (c) ( $\mathbf{1 0} \mathbf{p t s )}$ Suppose now we have $X$ and $Y$ with the same Gaussian marginals $f_{X}(x)$ and $f_{Y}(y)$ , and $\mu=0, \sigma^{2}=1$ . Further, we are told that $X$ and $Y$ are jointly Gaussian and $C_{X Y}=\frac{1}{2}$ . Find $f_{X \mid Y}(x \mid y)$ . How does your answer compare with the i.i.d. case stated in the original question above with $\mu=0, \sigma^{2}=1$ ?

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Problem 262

The given table is the probability distribution of the number of left handed (LH) students in a class of size $\mathbf{6}$ , given that the probability that a person is left handed is $\mathbf{2 0} \%$ . \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline $x$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline $P(X=x)$ & 0.1074 & 0.2684 & 0.3020 & 0.2013 & 0.0881 & 0.0264 & 0.0064 \\ \hline \end{tabular}
What is the probability of having 5 LH students in a class?

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Problem 263

The given table is the probability distribution of the number of left handed (LH) students in a class of size $\mathbf{6}$ , given that the probability that a person is left handed is $20 \%$ . \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline $x$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline $P(X=x)$ & 0.1074 & 0.2684 & 0.3020 & 0.2013 & 0.0881 & 0.0264 & 0.0064 \\ \hline \end{tabular}
What is the probability of having less than $\mathbf{3} \mathrm{LH}$ students in a class?

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Problem 264

Compute the critical value $z_{\alpha / 2}$ that corresponds to a $81 \%$ level of confidence. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2), $z_{\alpha / 2}=$ $\square$ (Round to two decimal places as needed.)

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Problem 265

Step 3: Choose alpha We will set alpha at . 05 0гटA Yz
How many degrees of freedom do we use in this example? (hint: look at the table
Step 4: Calculate the test statistic, or just look at the table below: Chi-square tests. \begin{tabular}{|c|c|c|c|} \hline Statistic & Value & Asymp. Sig. (2-tailed) & \\ \hline Pearson Chi-Square & 23.24 & .026) & Leve \\ \hline Likelihood Ratio & 20.31 & 062 & \\ \hline Linear-by-Linear Association & 7.77 & .005 & \\ \hline N of Valid Cases & 20 & & \\ \hline \end{tabular}

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Problem 266

In a survey, 600 adults in a certain country were asked how many hours they worked in the previous week. Based on the results, a $95 \%$ confidence interval for mean number of hours worked was lower bound: 41.2 and upper bound: 43.6 . Which of the following represents a reasonable interpretation o the result? For those that are not reasonable, explain the flaw. Complete parts (a) through (d) below. D. Flawed. This interpretation implies that the mean is only for last week. (b) We are $95 \%$ confident that the mean number of hours worked by adults in this country in the previous week was between 41.2 hours and 43.6 hours A. Correct. This interpretation is reasonable. B. Flawed. This interpretation implies that the population mean varies rather than the interval. C. Flawed. This interpretation does not make it clear that the $95 \%$ is the probability that the mean is within the interval. D. Flawed. This interpretation makes an implication about individuals rather than the mean. Clear all Check answe

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Problem 267

```latex A teacher gave two versions of a quiz, form 1 and form 2, to random samples of sociology students. She wanted to test whether the mean scores would be different if they were given to all sociology students. Here are the raw data.
Form 1 scores: 90, 83, 81, 73, 70, 67, 63, 63, 59, 57, 56, 55, 54, 50, 49, 32, 24, 6.
Form 2 scores: 100, 100, 100, 98, 91, 88, 73, 68, 66, 64, 61, 61, 61, 60, 49, 43, 22.
\begin{enumerate} \item[(a)] Compute the following, rounding to two decimal places. \begin{itemize} \item $t=$ \_\_\_\_\_\_\_ \item $p$ -value $=$ \_\_\_\_\_\_\_ \end{itemize} \item[(b)] Circle the words that make an appropriate conclusion, using $\alpha=0.05$ . REJECT / DON'T REJECT the NULL / ALTERNATIVE hypothesis. There IS / IS NOT statistically significant evidence that the mean scores would be THE SAME / DIFFERENT. \end{enumerate}
Skill: Estimate $\bar{x}_{1}-\bar{x}_{2}$ and the $p$ -value from a sketch of the sampling distribution.
For each completed sampling distribution for the difference of two means: \begin{enumerate} \item[(a)] Was it a one or two-tailed test? \item[(b)] Write the hypotheses. \item[(c)] What was the SEEsT? \item[(d)] What was the value of $\bar{x}_{1}-\bar{x}_{2}$ ? \item[(e)] Estimate the $p$ -value (roughly). \item[(f)] Should the null hypothesis be rejected? YES / NO \end{enumerate}
\begin{enumerate} \item[4.] \begin{enumerate} \item[(a)] \_\_\_\_\_\_ \item[(b)] \_\_\_\_\_\_ \item[(c)] \_\_\_\_\_\_ \item[(d)] \_\_\_\_\_\_ \item[(e)] \_\_\_\_\_\_ \item[(f)] YES / NO \end{enumerate} \item[5.] \begin{enumerate} \item[(a)] \_\_\_\_\_\_ \item[(b)] \_\_\_\_\_\_ \item[(c)] \_\_\_\_\_\_ \item[(d)] \_\_\_\_\_\_ \item[(e)] \_\_\_\_\_\_ \item[(f)] YES / NO \end{enumerate} \end{enumerate} ```

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Problem 268

Apply the Distributive Property to determine the missing number.
7. $3(4+5)=3 \cdot 4+3$ . $\qquad$ 8. $5(7-9)=5(7)-$ $\qquad$ (9)
9. $-4(8+y)=-4($ $\qquad$ ) $-4 y$
10. $-7(x-6)=$ $\qquad$ $(x)-$ $\qquad$
11. $5(37)=5 \cdot 30+5$ . $\qquad$ 12. $5(37)=5 \cdot 40-5$ . $\qquad$ Which expression(s) are not equivalent to the given expression?
13. $3(x+4)$
14. $-4(3+5)$ A. $3 \cdot x+3 \cdot 4$ A. $-4(3)+(-4) 5$ B. $3 x+4$ B. $-12+(-20)$ C. $3 x+12$ C. $-4(3)-(-4) 5$ D. $3 x+7$ D. -32
Jse the Distributive Property to write an equivalent expression.
15. $4(x-2)$
16. $3(a+7)$
17. $-5(b+9)$
18. $-8(m-4)$
19. $2(10-2)$
20. $-3(20+3)$ Exercises

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Problem 269

An NHANES report gives data for 641 men aged $20-29$ years. The BMI of these 641 men was $\bar{x}=25.6$ . On the basis of this sample, we want to estimate the BMI $\mu$ in the population of all 23.2 million American men in this age group. Treat these data as an SRS from a Normally distributed population with standard deviation $\sigma=7.2$ .
Source adapted from: Adapted from Fryar C. D., et al., Anthropometric reference data for children and adults: United States, 2011-2014. National Center for Health Statistics. Vital Health Statistics 3(2016), at htips:/www. ode.gov/nchs/data/ series/mr_04sr03_039.pAf.
Compare the three margins of error. How does increasing the sample size change the margin of error of a confidence interval when the confidence level and population standard deviation remain the same? Margin of error remains the same as $n$ increases. Margin of error is unaffected by the sample size $n$ . Margin of error increases as $n$ increases. Margin of error decreases as $n$ increases.

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Problem 270

Part 1 of 2 Points: 0 of 1
The heights of fully grown trees of a specific species are normally distributed, with a mean of 66.0 feet and a standard deviation of 7.00 feet Random samples of size 10 are drawn from the population. Use the central limit theorem to find the mean and standard error of the sampling distribution. Then sketch a graph of the sampling distribution.
The mean of the sampling distribution is $\mu_{\mathrm{x}}=$ $\square$ .
The standard error of the sampling distribution is $\sigma_{\bar{x}}=$ $\square$ (Round to two decimal places as needed) Clear all Check answ

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Problem 271

The heights of fully grown trees of a specific species are normally distributed, with a mean of 52.5 feet and a standard deviation of 5.75 feet. Random samples of size 17 are drawn from the population. Use the central limit theorem to find the mean and standard error of the sampling distribution. Then sketch a graph of the sampling distribution.
The mean of the sampling distribution is $\mu_{\bar{x}}=$ $\square$ 7.
The standard error of the sampling distribution is $\sigma_{\bar{x}}=$ $\square$ (Round to two decimal places as needed.)

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Problem 272

Here is a frequency distribution table (FDT) for a small data set: \begin{tabular}{|r|r|} \hline data value & frequency \\ \hline 27 & 5 \\ \hline 28 & 6 \\ \hline 29 & 2 \\ \hline 30 & 7 \\ \hline 31 & 3 \\ \hline \end{tabular}
Find the following measures of central tendency. mean $(\bar{x})=$ 30.7 $\square$ (Please show your answer to one decimal place.) median $=$ $\square$ 28 (Please enter an exact answer.) mode $=$ $\square$ 30 0 (Please enter an exact answer.)

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Problem 273

Andrea and Barsha are middle-distance runners for their school's track team. Andrea's time $A$ in the 400-meter race on a randomly selected day is approximately Normally distributed with a mean of 62 seconds and a standard deviation of 0.8 second. Barsha's time $B$ in the 400-meter race on a randomly selected day is approximately Normally distributed with a mean of 62.8 seconds and a standard deviation of 1 second. Assume that $A$ and $B$ are independent random variables.
What is the probability that Barsha beats Ashley in the 400 -meter race on a randomly selected day? 0.266 0.0368 0.734 0.00003 0.3284

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Problem 274

\begin{tabular}{l} $\frac{y}{0}$ \\ \hline \end{tabular}
The number of calories in a 1-ounce serving of a certain breakfast cereal is a random variable with mean 110 and standard deviation 10. The number of calories in a cup of whole milk is a random variable with mean 140 and standard deviation 12 . For breakfast, you eat 1 ounce of the cereal with $1 / 2$ cup of whole milk. Let $T$ be the random variable that represents the total number of calories in this breakfast.
The mean of $T$ is 110 140 250 180 195

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Problem 275

QUESTION 10
For a standard normal distribution, find the percentage of data that are between 2 standard deviations below the mean and 3 standard deviations above the mean. (Please enjoy my hand-drawn visual hint!) A. $95.49 \%$ B. 99.74\% C. $97.59 \%$ D. $102.15 \%$

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Problem 276

Find the $z$ -score that corresponds to the shaded area: A. -0.22 B. -0.41 C. -0.29 D. -0.33 t

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Problem 277

10.77 An experiment is conducted to determine if the use of a special chemical additive with a standard fertilizer accelerates plant growth. Ten locations are included in the study. At each location, two plants growing in close proximity are treated. One is given the standard fertilizer, the other the standard fertilizer with the chemical additive. Plant growth after four weeks is measured in centimeters. Do the following data substantiate the claim that use of the chemical additive accelerates plant growth? State the assumptions that you make and devise an appropriate test of the hypothesis. Take $\alpha=.05$ . \begin{tabular}{l|cccccccccc} \hline & \multicolumn{8}{|c}{ Location } \\ \cline { 2 - 10 } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline \begin{tabular}{c} Without \\ additive \\ \begin{tabular}{c} With \\ additive \end{tabular} \end{tabular} 20 & 23 & 17 & 22 & 19 & 32 & 25 & 18 & 21 & 19 \\ \hline \end{tabular}

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Problem 278

For the following probability distribution of number of left handed (LH) students in a class of size eight, when $p=$ 0.04 , the probability that class has at least one LH students, is: \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline $\mathrm{P}(\mathrm{X}=\mathrm{x})$ & p & 3 p & 5 p & 6 p & 4 p & 2 p & 2 p & p & p \\ \hline \end{tabular} a) 0.28 b) 0.64 c) 0.36 d) 0.96

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Problem 279

Your answer is partially correct.
Is a t-Distribution Appropriate? A sample with size $n=12$ has $\bar{x}=7.6$ and $s=1.6$ . The dotplot for this sample is given below.
Indicate whether or not it is appropriate to use the $t$ -distribution.
Yes $\leqslant$
If it is appropriate, give the degrees of freedom for the $t$ -distribution and give the estimated standard error. If it is not appropriate, enter -1 in both of the answer fields below.
Enter the exact answer for the degrees of freedom and round your answer for the standard error to two decimal places. $d f=$ i $\square$ standard error = $\square$ eTextbook and Media Hint Attempts: 1 of 5 used Submit Answer

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Problem 280

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Current Attempt in Progress Is a t-Distribution Appropriate? A sample with size $n=75$ has $\bar{x}=18.92$ , and $s=10.1$ . The dotplot for this sample is given below.
Indicate whether or not it is appropriate to use the $t$ -distribution. $\square$ If it is appropriate, give the degrees of freedom for the $t$ -distribution and give the estimated standard error. If it is not appropriate, enter -1 in both of the answer fields below.
Enter the exact answer for the degrees of freedom and round your answer for the standard error to two decimal places. $d f=$ $\square$ i standard error = $\square$ i eTextbook and Media Save for Later Attempts: 0 of 5 used Submit Answer

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Problem 281

A survey found that people keep their televisions an average of 5.8 years. The standard deviation is 0.78 years. Find the percentage of people that owned theil TV for the given amount of time. Assume the random variable is normally distributed. Refer to the table of values ( Area Under the Standard Normal Distribution) as needed.
Part: $0 / 3$ $\square$
Part 1 of 3 (a) More than 8.14 years
The percentage of people who owned his or her TV for more than 8.14 years is $\square$ \%.

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Problem 282

A study showed that $\mathbf{8 \%}$ of American teenagers have tattoos. $\mathbf{2 8}$ teenagers are randomly selected. What is the probability that exactly $\mathbf{2}$ will have a tattoo? (Round the answer up to 4 decimal places) $\square$ Done

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Problem 283

A fair coin is tossed six times. Find the mean, variance and standard deviations of number of heads obtained. (Round the answers upto 3 decimal places)
Click here to enter an

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Problem 284

For a non-standard normal distribution with $\boldsymbol{\mu}=\mathbf{3 0 0}$ and $\boldsymbol{\sigma}=\mathbf{6 0}$ , find the probability that $X$ assumes values less than 211. (Round answer up to $\mathbf{4}$ decimal places.)
Table for required value of $z$ Probability = $\square$ Done

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Problem 285

According to an online source, the mean time spent on smartphones daily by adults in a country is 2.55 hours. Assume that this is correct and assume the standard deviation is 1.2 hours. Complete parts (a) and (b) below. a. Suppose 150 adults in the country are randomly surveyed and asked how long they spend on their smartphones daily. The mean of the sample is recorded. Then we repeat this process, taking 1000 surveys of 150 adults in the country. What will be the shape of the distribution of these sample means?
The distribution will be $\square$ because the values will be $\square$

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Problem 286

Match each of the normal curves to its mean $\mu$ and standard deviation $\sigma$ .
Part 1 of 2 (a)
Normal curve with $\square$ (Choose one) $\begin{array}{ll} \mu=4, & \sigma=1 \\ \mu=4, & \sigma=3 \end{array}$

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Problem 287

Let's go back to the television question: According to the Buckert and Howell research firm the time spent by kids watching television per year can be modelled by a normal distribution with a mean of 1200 hours and a standard deviation of 180 hours.
What percent of children watch between 1000 and 1500 hours of television? Shade the distribution belon
1. The average reading score for BSHS students is 580 with a standard deviation of 50 points. What percent of students are: a) Between 500 and 600? d) More than 680 ? b) Between 650 and 750 ? c) Less than 450 ?

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Problem 288

Find the mean (expected value) of the probability distribution. \begin{tabular}{|c|c|} \hline $x$ & $P(x)$ \\ \hline 75 & .12 \\ \hline 80 & .23 \\ \hline 85 & .42 \\ \hline 90 & .11 \\ \hline 95 & .12 \\ \hline \end{tabular} 85 83.2 87.1 84.4

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Problem 289

A hotel manager assumes that $18 \%$ of the hotel rooms are booked. If the manager is correct, what is the probability that the proportion of rooms booked in a sample of 480 rooms would be less than $15 \%$ ? Round your answer to four decimal places.
Answer Tables Keypad
How to enter your answer (opens in new window) Keyboard Shortcuts

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Problem 290

$v \sqrt{44(0.2)(0.8)}$
10. Suppose the probability of a major earthquake on a given day is 1 out of 15,000 . Use the Poisson distribution to approximate the probability that there will be at least one major earthquake in the next 2000 days. poissun 1

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Problem 291

The length of human pregnancies is approximately normal with mean $\mu=266$ days and standard deviation $\sigma=16$ days. Complete parts (a) through (f).
Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) What is the probability that a randomly selected pregnancy lasts less than 258 days?
The probability that a randomly selected pregnancy lasts less than 258 days is approximately . $\square$ (Round to four decimal places as needed.)

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Problem 292

The army of a certain country fired 1500 missiles. The probability that a fired missile will hit a critical infrastructure target is 2.9 per mille. Determine the (exact!) probability that at least two missiles will hit critical infrastructure targets. Please provide the result rounded to at least FOUR decimal digits.
Answer: $\square$ $\qquad$
Continuing the calculations from the previous problem please approximate the calculated probability using the Poisson theorem. Provide the approximation result rounded to FOUR decimal places.

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Problem 293

In a single fight in his category, a certain boxer wins with probability 0.31 , loses with probability 0.37 , and draws the remaining fights. Calculate the probability that in 12 fights, he will have 3 wins and 2 draws. Provide the result rounded to THREE decimal places.

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Problem 294

Which of the following is true if the given tree diagram represents independent events? A. The probability of buying nonfiction is larger than buying fiction. B. The probability of buying fiction versus nonfiction is not the sam regardless of whether or not the person buys a hardcover or paperback. C. The probability of buying a hardcover is less than buying a paperback D. The probability of buying fiction versus nonfiction is the same regardless of whether or not the person buys a hardcover or paperback.

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Problem 295

Os seguintes dados dizem respeito a um inquérito feito numa escola sobre o número de vezes que os alunos do $10 .^{\circ}$ ano utilizaram a biblioteca escolar no primeiro período. \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline \begin{tabular}{l} Número de \\ utilizações da \\ biblioteca escolar \end{tabular} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline Número de alunos & 6 & 26 & 24 & 14 & 12 & 8 & 4 & 10 & 2 & 8 & 6 \\ \hline \end{tabular} 7.1. Construa a respetiva tabela de frequências relativas. Apresente os valores obtidos com duas casas decimais.
2. Indique, se existir, a moda deste conjunto de dados.
3. Determine a mediana do conjunto de dados apresentado.
De uma empresa de fabrico de materiais de construção, sabe-se que o departamento financeiro é constituído por 19 colaboradores, cuja média das suas idades é 36 e a amplitude da distribuição das mesmas é 30.
Qual dos seguintes diagramas de caule-e-folhas pode representar as idades dos colaboradores do departamento financeiro daquela empresa? (A) Idades dos colaboradores (B) Idades dos colaboradores \begin{tabular}{l|lllllllll} 2 & 2 & 2 & 4 & 4 & & & & & \\ 3 & 1 & 2 & 2 & 3 & 4 & 6 & 8 & 8 & 8 \\ 4 & 0 & 2 & 6 & & & & & & \\ 5 & 0 & 0 & 2 & & & & & & \end{tabular} \begin{tabular}{l|lllllllll} 2 & 3 & 3 & 4 & 5 & & & & \\ 3 & 1 & 1 & 2 & 3 & 4 & 5 & 8 & 8 & 8 \\ 4 & 2 & 2 & 4 & & & & & & \\ 5 & 0 & 0 & 1 & & & & & & \end{tabular}
2| 3 significa 23 anos (C) Idades dos colaboradores
2|3 significa 23 anos (D) Idades dos colaboradores \begin{tabular}{l|lllllllll} 2 & 3 & 4 & 4 & 6 & & & & & \\ 3 & 1 & 2 & 2 & 3 & 4 & 6 & 8 & 9 & 9 \\ 4 & 2 & 4 & 8 & & & & & & \\ 5 & 0 & 0 & 3 & & & & & & \end{tabular} \begin{tabular}{l|lllllllll} 2 & 3 & 4 & 4 & 4 & & & & & \\ 3 & 1 & 2 & 2 & 3 & 4 & 6 & 8 & 9 & 9 \\ 4 & 2 & 4 & 8 & & & & & & \\ 5 & 0 & 0 & 1 & & & & & & \end{tabular} 2/3 significa 23 anos 2/3 significa 23 anos

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Problem 296

6. De uma empresa de fabrico de materiais de construção, sabe-se que o departamento financeiro é constituído por 19 colaboradores, cuja média das suas idades é 36 e a amplitude da distribuição daş mesmas é 30. 6.1. Qual dos seguintes diagramas de caule-e-folhas pode representar as idades dos colaboradores do departamento financeiro daquela empresa? (A) Idades dos colaboradores (B) Idades dos colaboradores \begin{tabular}{l|llllllllll} 2 & 2 & 2 & 4 & 4 & & & & & \\ 3 & 1 & 2 & 2 & 3 & 4 & 6 & 8 & 8 & 8 \\ 4 & 0 & 2 & 6 & & & & & & \\ 5 & 0 & 0 & 2 & & & & & & \end{tabular} \begin{tabular}{l|lllllllll} 2 & 3 & 3 & 4 & 5 & & & & & \\ 3 & 1 & 1 & 2 & 3 & 4 & 5 & 8 & 8 & 8 \\ 4 & 2 & 2 & 4 & & & & & & \\ 5 & 0 & 0 & 1 & & & & & & \end{tabular} $2 \mid 3$ significa 23 anos 2/3 significa 23 anos (C) Idades dos colaboradores \begin{tabular}{l|llllllllll} 2 & 3 & 4 & 4 & 6 & & & & & \\ 3 & 1 & 2 & 2 & 3 & 4 & 6 & 8 & 9 & 9 \\ 4 & 2 & 4 & 8 & & & & & & \\ 5 & 0 & 0 & 3 & & & & & & \end{tabular} (D) Idades dos colaboradores
2/3 significa 23 anos $\begin{array}{l|lllllllll} 2 & 3 & 4 & 4 & 4 & & & & & \\ 3 & 1 & 2 & 2 & 3 & 4 & 6 & 8 & 9 & 9 \\ 4 & 2 & 4 & 8 & & & & & & \\ 5 & 0 & 0 & 1 & & & & & & \end{array}$

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Problem 297

Find the critical tscore to three decimal places when the Confidence Level is $93 \%$ and the sample size is 32 A. 2.245 B. 2.891 C. 1.682 D. 1.877

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Problem 298

18. A population has a mean of 200 and a standard deviation of 50 . A sample of size 1 will be taken and the sample mean $\bar{x}$ will be used to estimate the population mean. a. What is the expected value of $\bar{x}$ ? b. What is the standard deviation of $\bar{x}$ ? c. Show the sampling distribution of $\bar{x}$ . d. What does the sampling distribution of $\bar{x}$ show?

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Problem 299

It is known that roughly 2/3 of all human beings have a dominant right foot or eye. Is there also right-sided dominance in kissing behavior? An article reported that in a random sample of 115 kissing couples, both people in 73 of the couples tended to lean more to the right than to the left. (Use a = 0.05.) USE SALT (a) If 2/3 of all kissing couples exhibit this right-leaning behavior, what is the probability that the number in a sample of 115 who do so differs from the expected value by at least as much as what was actually observed? (Round your answer to four decimal places.) (b) Does the result of the experiment suggest that the 2/3 figure is implausible for kissing behavior? State the appropriate null and alternative hypotheses. Ho: P = 2/3 Hp < 2/3 Ho P = 2/3 H: p + 2/3 O Ho: p = 2/3 HP ≤ 2/3 OHP = 2/3 H:p> 2/3 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) == P-value =

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Problem 300

Fill out the black to make the given table below a probability distribution. \begin{tabular}{|l|ll|} \hline $x$ & $P(x)$ & \\ \hline 0 & 0 & \\ \hline 1 & 0.03 & \\ \hline 2 & 0.18 & \\ \hline 3 & & $\sigma$ \\ \hline 4 & 0.34 & \\ \hline \end{tabular} Submit Question

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Distribution

Problem 201

Problem 202

Problem 203

Problem 204

Problem 205

Question \#2 (pg. 183) Compute the mean and variance of the following discrete probability distribution. \begin{tabular}{|cc|} \hline X\mathbf{X}X & P(x)\mathbf{P}(\mathbf{x})P(x) \\ \hline 2 & .5 \\ 8 & .3 \\ 10 & .2 \\ \hline \end{tabular}

Problem 206

Use the Standard Normal Table or technology to find the zzz-score that corresponds to the following cumulative area. 0.90060.90060.9006The cumulative area corresponds to the z-score of □\square□ (Round to three decimal places as needed.)

Problem 207

Problem 208

Find the z-score that has 10.2%10.2 \%10.2% of the distribution's area to its left.The z-score is □\square□ (Round to two decimal places as needed.)

Problem 209

Find the z-score that has 3.533%3.533 \%3.533% of the distribution's area to its left.The z-score is □\square□ (Round to two decimal places as needed.)

Problem 210

Problem 211

Problem 212

Problem 213

Problem 214

Problem 215

3. 21. Supozojmë se XXX ka densitet f(x)=e−x,x>0f(x)=e^{-x}, \quad x>0f(x)=e−x,x>0 (a) Llogaritni funksionin prodhues të momenteve të XXX dhe gjeni pritjen matematike, mesataren dhe dispersionin. (b) Gjeni pritjen matematike drejtpërsëdrejti nga përkufizimi.

Problem 216

Problem 217

Problem 218

Problem 219

Problem 220

Problem 221

Problem 222

Problem 223

Problem 224

Problem 225

Problem 226

Problem 227

Problem 228

Problem 229

Problem 230

Problem 231

Problem 232

Problem 233

Problem 234

Problem 235

Problem 236

Problem 237

Problem 238

Problem 239

Problem 240

Problem 241

Problem 242

Problem 243

The probability mass function of a random variable XXX is given by p(i)=cλii!,i=0,1,2,…p(i)=\frac{c \lambda^{i}}{i!}, \mathrm{i}=0,1,2, \ldotsp(i)=i!cλi​,i=0,1,2,…, where λ\lambdaλ is som positive value. Find ia) P{X=0}P\{X=0\}P{X=0} and (b) P{X>2}P\{X>2\}P{X>2}.

Problem 244

Problem 245

Problem 246

\text{Refer to Exercise 39. Define event } A : \text{ sum is 5. Find } P(A). \text{ (The scenario involves rolling 2 four-sided dice.)}

Problem 247

Problem 248

السؤال الثاني:أوجد :1. المدى ؟2. التباين ؟3. الانحراف المعياري ؟

Problem 249

Problem 250

Problem 251

Problem 252

The lifespan of some macaws in captivity is normally distributed. Their lifespan has a mean of 50 years and a standard deviation of 8 years.What is the probability of a macaw with a lifespan greater than 60 years?

Problem 253

Problem 254

Problem 255

Problem 256

Problem 257

Problem 258

Problem 259

Problem 260

Problem 261

Problem 262

Problem 263

Problem 264

Problem 265

Problem 266

Problem 267

Problem 268

Problem 269

Problem 270

Question \#2 (pg. 183) Compute the mean and variance of the following discrete probability distribution. \begin{tabular}{|cc|} \hline $\mathbf{X}$ & $\mathbf{P}(\mathbf{x})$ \\ \hline 2 & .5 \\ 8 & .3 \\ 10 & .2 \\ \hline \end{tabular}

Use the Standard Normal Table or technology to find the $z$ -score that corresponds to the following cumulative area. $0.9006$
The cumulative area corresponds to the z-score of $\square$ (Round to three decimal places as needed.)

Find the z-score that has $10.2 \%$ of the distribution's area to its left.
The z-score is $\square$ (Round to two decimal places as needed.)

Find the z-score that has $3.533 \%$ of the distribution's area to its left.
The z-score is $\square$ (Round to two decimal places as needed.)

3. 21. Supozojmë se $X$ ka densitet $f(x)=e^{-x}, \quad x>0$ (a) Llogaritni funksionin prodhues të momenteve të $X$ dhe gjeni pritjen matematike, mesataren dhe dispersionin. (b) Gjeni pritjen matematike drejtpërsëdrejti nga përkufizimi.

The probability mass function of a random variable $X$ is given by $p(i)=\frac{c \lambda^{i}}{i!}, \mathrm{i}=0,1,2, \ldots$ , where $\lambda$ is som positive value. Find ia) $P\{X=0\}$ and (b) $P\{X>2\}$ .

السؤال الثاني:
أوجد :
1. المدى ؟
2. التباين ؟
3. الانحراف المعياري ؟

The lifespan of some macaws in captivity is normally distributed. Their lifespan has a mean of 50 years and a standard deviation of 8 years.
What is the probability of a macaw with a lifespan greater than 60 years?