Distribution

Problem 1101

A magazine includes a report on the energy costs per year for 32 -inch liquid crystal display (LCD) televisions. The article states that 14 randomly selected 32 -inch LCD televisions have a sample standard deviation of $\$ 3.56$ . Assume the sample is taken from a normally distributed population. Construct $90 \%$ confidence intervals for (a) the population variance $\sigma^{2}$ and (b) the population standard deviation $\sigma$ . Interpret the results. (a) The confidence interval for the population variance is $\square$ , ). (Round to two decimal places as needed.) Interpret the results. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.) A. With $10 \%$ confidence, you can say that the population variance is between
$\square$ and $\square$ B. With $90 \%$ confidence, you can say that the population variance is less than C. With $90 \%$ confidence, you can say that the population variance is between $\square$ D. With $10 \%$ confidence, you can say that the and $\square$ population variance is greater than

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Problem 1102

Find the probability that a randomly chosen American has type B blood, given that $15\%$ of Americans have type B.

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Problem 1103

Is a score of $X=70$ extreme for a population with mean $\mu=50$ and $\sigma=20$ ? How about with $\sigma=5$ ?

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Problem 1104

Find the probability that a random American has type B blood ( $15\%$ ) and the probability of having type A or B.

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Problem 1105

Find the probability of randomly selecting a school with 100 or fewer computers. Round to 3 decimal places.

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Problem 1106

In 2002, the median home price was \$ 184,200. Which standard deviation is most plausible: \$ 2000, \$ 60,000, or \$ 1,000,000? Why?

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Problem 1107

For 57 female athletes, $\bar{x}=72.4$ and $s=13.6$ . Use the empirical rule to find the interval for $68\%$ of data.

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Problem 1108

Data from 57 female athletes shows $\bar{x}=72.4$ and $s=13.6$ . Use the empirical rule to find intervals for 68% and 95%.

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Problem 1109

For 57 female athletes, $\bar{x}=72.4$ and $s=13.6$ . Use the empirical rule to find intervals for 68%, 95%, and nearly all data.

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Problem 1110

What is the probability that Ava is assigned the numbers 1, 5, or 10 out of 16 possible tryout numbers?

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Problem 1111

Find the percentage of scores between 158 and $872$ in a normal distribution with mean 515 and std dev 119.

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Problem 1112

A standardized test's math scores have a mean of 515 and a standard deviation of 119. Find the percentages for the given ranges.

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Problem 1113

A standardized test has scores with a mean of 515 and a standard deviation of 119. Find the percentages for parts (a), (b), and (c).

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Problem 1114

Find $n$ and $\Sigma X$ for the frequency distribution: $x$ : 5-2, 4-2, 3-2, 2-4, 1-1.

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Problem 1115

Approximate the median from the given frequency distribution table. Report it as the midpoint of the median class.

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Problem 1116

Approximate the median of the given frequency distribution. Report as the midpoint of the median class.

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Problem 1117

Approximate the median from the given frequency distribution table. Report the midpoint of the median class.

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Problem 1118

What is the minimum number of prizes, all powers of 2, needed to total \$ 988?

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Problem 1119

Determine the expected shape of the histogram for student scores (out of 100) on a difficult exam: symmetric, skewed right, or skewed left?

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Problem 1120

For 57 female athletes, $\bar{x}=74.8$ and $s=13.8$ . Use the empirical rule to find the intervals for 68%, 95%, and nearly all data.

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Problem 1121

Identify the type of distribution: right tail longer than left tail. Options: skewed right, symmetric, skewed left, not skewed, none.

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Problem 1122

Given data for 57 female athletes shows $\bar{x}=86.1$ and $s=13.3$ . Use the empirical rule to find intervals for 68%, 95%, and nearly all.

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Problem 1123

QUESTION 38 1 POINT Given the plot of normal distributions $A$ and $B$ below, which of the following statements is true? Select all correct answers.
Select all that apply: $A$ has the larger mean. $B$ has the larger mean. The means of $A$ and $B$ are equal. $A$ has the larger standard deviation. $B$ has the larger standard deviation.

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Problem 1124

Calories in Cheeseburgers The number of calories in a random selection of cheeseburgers from 10 fast food restaurants is listed. \begin{tabular}{lllll} 497 & 533 & 536 & 513 & 505 \\ 441 & 442 & 510 & 482 & 478 \end{tabular} Send data to Excel
Is there sufficient evidence to conclude that the variance differs from 700? Use the 0.01 level of significance. Assume the variables are approximately normally distributed.
Part 1 of 5 (a) State the hypotheses and identify the claim with the correct hypothesis. $\begin{array}{l} H_{0}: \sigma^{2}=700 \text { not claim } \\ H_{1}: \sigma^{2} \neq 700 \text { claim } \end{array}$
This hypothesis test is a two-tailed test.
Part 2 of 5 (b) Find the critical value(s). Round the answer(s) to at least three decimal places. If there is more than one critical value, separate them with commas. $\text { Critical value(s): } 1.735,23.589$
Part: $2 / 5$
Part 3 of 5 (c) Compute the test value. Round the answer to at least three decimal places, $x^{2}=$ $\square$

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Problem 1125

Calories in Cheeseburgers The number of calories in a random selection of cheeseburgers from 10 fast food restaurants is listed. \begin{tabular}{lllll} 497 & 533 & 536 & 513 & 505 \\ 441 & 442 & 510 & 482 & 478 \end{tabular}
Send data to Excel Is there sufficient evidence to conclude that the variance differs from 700? Use the 0.01 level of significance. Assume the variables are approximately normally distributed.
Part 1 of 5 (a) State the hypotheses and identify the claim with the correct hypothesis. $\begin{array}{l} H_{0}: \sigma^{2}=700 \text { not claim } \quad \\ H_{1}: \sigma^{2} \neq 700 \text { claim } \end{array}$
This hypothesis test is a two-tailed $\boldsymbol{\nabla}$ test.
Part 2 of 5 (b) Find the critical value(s). Round the answer(s) to at least three decimal places. If there is more than one critical value, separate them with commas.
Critical value(s): $1.735,23.589$
Part: $2 / 5$
Part 3 of 5 (c) Compute the test value. Round the answer to at least three decimal places. $\begin{array}{l} \chi^{2}= \\ \square \end{array}$

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Problem 1126

(1 point) The daily demand $x$ for a certain product is a random variable with the probability density function $f(x) = \frac{6}{8}x(2-x)$ for $0 \le x \le 2$ .
Determine the expected value of demand: 1
Determine the standard deviation of demand: 0.447
Determine the probability that $x$ is within one standard deviation of the mean: 0.430

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Problem 1127

A researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The table shows the results for the number of bacteria per cubic foot for both types of rooms.
Carpeted | Uncarpeted ------- | -------- 13.7 | 11.8 6.9 | 8.2 7.4 | 13.1 8.9 | 5.3 7.9 | 7.8 8.5 | 4.1 10.7 | 12.7 14.1 | 5.4
Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the $\alpha = 0.01$ level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers. State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms. A. $H_0: \mu_1 = \mu_2$ $H_1: \mu_1 > \mu_2$ B. \(H_0: \mu_1 < \mu

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Problem 1128

$54 \%$ of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four. (a) $P(5)=$ $\square$ (Round to three decimal places as needed.)

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Problem 1129

Decide which of the following statements are true.
Answer
There are an unlimited number of normal distributions.
The line of symmetry for all normal distributions is $x = 0$ .
The total area under a normal distribution curve equals $1$ .
The inflection points for any normal distribution are three standard deviations on either side of the mean.

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Problem 1130

Avg 28 Stdev 3 What 2 values will 95\% of days be

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Problem 1131

Avg 28 Stdev 3 What 2 values will 95% of days be

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Problem 1132

Find the critical value For confidence level of $98\%$

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Problem 1133

$\text{A sample of } 150 \text{ U.S. college students had a mean age of } 22.77 \text{ years. Assume the population standard deviation is } \sigma = 4.42 \text{ for the mean age of U.S. college students.}$ $\text{Calculate the 90\% confidence interval for the mean age of U.S. college students. Round the answers to at least two decimal places.}$

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Problem 1134

A lawncare technician believes the actual lifetime to be different than 250 hours. A test is made of $H_0: \mu = 250$ versus $H_1: \mu \neq 250$ . The null hypothesis is not rejected. State an appropriate conclusion. There (Choose one) enough evidence to conclude that the mean lifetime is (Choose one) 250 hours.

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Problem 1135

A simple random sample of size 35 has mean $x = 3.49$ . The population standard deviation is $\sigma = 1.59$ . Construct a 90% confidence interval for the population mean.
The parameter is the population mean.
The correct method to find the confidence interval is the $t$ method.

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Problem 1136

If $X$ is a binomial random variable with $n$ trials and success probability $p$ , then as $n$ gets larger, the distribution of $X$ becomes (Choose one) skewed, less

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Problem 1137

Assume the variable $X$ is normally distributed with mean 120 and standard deviation 13. Find $P(100 < X < 155)$ NOTE: You must add an attachment to this question that shows all of your work in getting the answer to receive credit.

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Problem 1138

Use the Cumulative Normal Distribution Table to find the $z$ -score for which the area to its left is $0.69$ . The $z$ -score for the given area is

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Problem 1139

(a) The following dotplot illustrates a sample. The dotplot reveals (Choose one) approximately norman outlier a large degree of skewness more than one distinct mode none of these features Therefore, we (Choose one)

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Problem 1140

(d) The following stem-and-leaf plot illustrates a sample. 4|6 5|5 6|2 7| 8|17 9|2445 10|011245569 11|58 The stem-and-leaf plot reveals (Choose one) from an approximately normal population. Therefore, we (Choose one)

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Problem 1141

$x$ | $P(x)$ ---|--- 56 | 0.3 66 | 0.8 76 | 0.2 86 | -0.3 Determine whether the table represents a discrete probability distribution. Explain why The table (Choose one) represent Send data to Excel

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Problem 1142

A true false quz with 10 questions was given to a statistics class. Following is the probability distribution for the score of a randomly chosen student mean score and interpret the result. Round the answers to two decimal places as needed.
$x$ | 5 | 6 | 7 | 8 | 9 | 10 --- | --- | --- | --- | --- | --- | --- $P(x)$ | 0.05 | 0.18 | 0.4 | 0.2 | 0.1 | 0.07
The mean is
If we were to give this quiz to more and more students, the mean score for these students would approach

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Problem 1143

Suppose that the New England Colonials baseball team is equally likely to win any particular game as not to win it. Suppose also that we choose a random sample of 30 Colonials games.
Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of games in the sample that the Colonials win by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. $\square$ (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your respons to at least three decimal places. $\square$

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Problem 1144

Determine whether the distribution represents a probability distribution.
$X$ | 3 | 7 | 10 $P(X)$ | 0.1 | 0.3 | -0.2
Send data to Excel
Part: 0 / 2
Part 1 of 2
The distribution (Choose one) a probability distribution. represents does not represent

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Problem 1145

Public health officials believe that 90.6% of children have been vaccinated against measles. A random survey of medical records at many schools across the country found that, among more than 13,000 children, only 89.8% had been vaccinated. A statistician would reject the 90% hypothesis with a P-value of $P = 0.022$ .
a) Explain what the P-value means in this context. b) The result is statistically significant, but is it important? Comment.
A. We concluded that the actual percentage of vaccinated children is below 90.6%. A 0.8% drop would probably not be considered noteworthy but in context, if 1,000,000 children are vaccinated each year a 0.8% difference accounts for 8000 more children not being vaccinated, which is important.
B. A 0.8% difference in child vaccinations in not important.
C. We conclude that the actual percentage of vaccinated children is below 90.6% and is about 89.8%. This drop is not important because only a 5% change or more can be considered important.

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Problem 1146

Often, frequency distributions are reported using unequal class widths because the frequencies of some groups would otherwise be small or very large. Consider the following data, which represent the daytime household temperature the thermostat is set to when someone is home for a random sample of $753$ households. Determine the class midpoint, if necessary, for each class and approximate the mean and standard deviation temperature. Click the icon to view the frequency distribution for the daytime household temperature.
Class | Class Midpoint ------- | -------- 61-64 | 65-67 | 68-69 | 70 | 71-72 | 73-76 | 77-80 |
Frequency distribution
Temperature $^\circ \text{F}$ | Frequency ------- | -------- 61-64 | 34 65-67 | 70 68-69 | 191 70 | 194 71-72 | 124 73-76 | 86 77-80 | 54
(Round to one decimal place as needed.)
The sample mean is $^{\circ}\text{F}$ . (Round to one decimal place as needed.)
The sample standard deviation is $^{\circ}\text{F}$ . (Round to one decimal place as needed.)

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Problem 1147

38 married couples without children are asked to report the number of times per year they initiate a date night. The men report initiating an average of 8.3 date nights with a standard deviation of 4.1, though it's possible they're overstating to make themselves look good. Is there significant evidence to conclude that married men without children initiate date night 7 times per year at the 0.05 significance level? Note that there's evidence that this distribution is skewed.
What are the hypotheses? $H_0: \mu \le 7$ vs $H_1: \mu > 7$ $H_0: \mu = 7$ vs $H_1: \mu \ne 7$ $H_0: \mu = 8.3$ vs $H_1: \mu \ne 8.3$ $H_0: \mu \le 8.3$ vs $H_1: \mu > 8.3$
What distribution does the test statistic follow? t with 39 degrees of freedom t with 37 degrees of freedom t with 38 degrees of freedom z
What is the value of the test statistic? Round to two decimal places. 1.96
What is probability statement for the p-value? $2P(T \ne \text{test statistic})$ $P(T > \text{test statistic})$ $2P(Z \ne \text{test statistic})$ $P(Z \ge \text{test statistic})$ None of the above

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Problem 1148

QUESTION 1 Provide an appropriate response. A placement exam for entrance into a math class yields a mean of 80 and a standard deviation of 10. The distribution of the scores is roughly bell-shaped. Use the Empirical Rule to find the percentage of scores that lie between 60 and 80. 68\% 95\% $34 \%$ 47.5\%

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Problem 1149

12. When four fair coins are tossed, what is the probability that the outcome will consist of two heads and two tails? (A) $\frac{1}{2}$ (B) $\frac{11}{20}$ (C) $\frac{1}{3}$ (D) $\frac{1}{4}$ (E) $\frac{3}{8}$

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Problem 1150

How many stores have fewer than 60 pairs of boots based on the stem-and-leaf plot?

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Problem 1151

Students weighed pumpkins for a contest. Create a boxplot and discuss why median and IQR are better than mean and SD for summary.

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Problem 1152

Data from a book fair shows the number of books bought by 20 youths. Find the mean, standard deviation, and $70^{\text{th}}$ percentile.

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Problem 1153

Given salaries of 30 employees, identify measures of central tendency: a) for proving underpayment, b) for proving fair pay, c) fairest measure.

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Problem 1154

Compare two data sets: I has mean \$245, SD \$30; II has mean 30 min, SD 5 min. a) Why use CV for comparison? b) Which has larger variation?

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Problem 1155

Find the percentage of values below $125$ in a normal distribution with mean $159$ and standard deviation $17$ .

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Problem 1156

Calculate the new mean age after subtracting 2 from 20.1 and the new standard deviation of ages. Convert mean height 165.4 cm to inches using 0.394.

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Problem 1157

Dante is taking a self-paced math class. His scores for each of the 17 quizzes during the academic year are shown below. Complete the grouped relative frequency distribution for the data. (Note that we are using a class width of 6.) Write each relative frequency as a decimal rounded to the nearest hundredth, not as a percentage.
Quiz score 85 84 73 77 88 75 71 89 87 73 89 87 85 72 86 81 80
Quiz score Relative frequency 66 to 71 72 to 77 78 to 83 84 to 89

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Problem 1158

A sample of size $n = 66$ is drawn from a normal population whose standard deviation is $\sigma = 6.2$ . The sample mean is $\overline{x} = 37.77$ .
Part: 0 / 2
Part 1 of 2
(a) Construct a 99% confidence interval for $\mu$ . Round the answer to at least two decimal places.
A 99% confidence interval for the mean is $\boxed{\phantom{00}} < \mu < \boxed{\phantom{00}}$ .

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Problem 1159

Español ek and Stone Mountain are schools in different states. The heights of students at Castle Creek have a population mean of 59.7 inches and a standard of 1.4 inches. The heights of students at Stone Mountain have a population mean of 56.7 inches with a standard deviation of 1.5 inches. For each distribution of the heights of students is clearly bell-shaped. student at Castle Creek and is 57 inches tall. Melissa is a student at Stone Mountain and is 53 inches tall. d the $z$ -scores of Maya's height as a student at Castle Creek and Melissa's height as a student at Stone Mountain. und your answers to two decimal places. -score of Maya's height: $\square$ -score of Melissa's height: $\square$ ative to her population, which student is taller? ose the best answer based on the $z$ -scores of the two heights.
Maya Melissa It is unclear which student is taller relative to her population

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Problem 1160

Researchers wanting to assess level of heel pain associated with a new footwear developed for those with plantar fasciitis. They randomly sample 120 people with a history of plantar fasciitis and 120 people without a history of plantar fasciitis and ask them to wear the shoes and report the level of heel pain (1-10) they experience after walking in the shoes for 2 hours. The average heel pain score for the group with plantar fasciitis was 1.4 and the average heel pain score for the group without plantar fasciitis was 1.2. The Levene's test for equality of variances had a $p$ value of 0.11. You know this means: The researchers should report the $t$ -test results for assuming equal variances The researchers should report the t-test results NOT assuming equal variances The researchers should reject the null hypothesis and report there is a difference in the average heel pain score The researchers should fail to reject the null hypothesis and conclude there is NOT a difference in the average heel pain score

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Problem 1161

Ihis question: 1 point(S) possible A data set includes 109 body temperatures of healthy adult humans having a mean of $98.2^{\circ} \mathrm{F}$ and a standard deviation of $0.62^{\circ} \mathrm{F}$ . Construct a $99 \%$ confidence interval estimate of the mean body temperatu humans. What does the sample suggest about the use of $986^{\circ} \mathrm{F}$ as the mean body temperature? Click here to view a t distribution table. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table.
What is the confidence interval estimate of the population mean $\mu$ ? $\square$ ${ }^{\circ} \mathrm{F}<\mu<$ $\square$ ${ }^{\circ} \mathrm{F}$ (Round to three decimal places as needed.) What does this suggest about the use of $986^{\circ} \mathrm{F}$ as the mean body temperature? A. This suggests that the mean body temperature is higher than $98.6^{\circ} \mathrm{F}$ B. This suggests that the mean body temperature is lower than $98.6^{\circ} \mathrm{F}$ C. This suggests that the mean body temperature could very possibly be $98.6^{\circ} \mathrm{F}$

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Problem 1162

Refer to the accompanying data display that results from a sample of airport data TInterval speeds in Mbps. Complete parts (a) through (c) below.
Click the icon to view a t distribution table. $\begin{array}{l} (13.046,22.15) \\ x=17.598 \\ S x=16.01712719 \\ n=50 \end{array}$ a. What is the number of degrees of freedom that should be used for finding the critical value $t_{\alpha / 2}$ ? $\mathrm{df}=$ (Type a whole number.)

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Problem 1163

$n = 28$ , $p = 0.55$ Mean: $\mu =$ Variance: $\sigma^2 =$ Standard deviation: $\sigma =$ Part 3 of 4

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Problem 1164

A pizza shop sells three sizes of pizza, and they track how often each size gets ordered along with how much they profit from each size. Let $X$ represent the shop's profit on a randomly selected pizza. Here's the probability distribution of $X$ along with summary statistics:
| | Small | Medium | Large | | :-------- | :---- | :----- | :---- | | $X$ = profit (\$) | 4 | 8 | 12 | | $P(X)$ | 0.18 | 0.50 | 0.32 |
Mean: $\mu_X = \$8.56$ Standard deviation: $\sigma_X = \$2.77$
The company is going to run a promotion where customers get $\$2$ off any size pizza. Assume that the promotion will not change the probability that corresponds to each size. Let $Y$ represent their profit on a randomly selected pizza with this promotion.
What are the mean and standard deviation of $Y$ ?
$\mu_Y =$ ______ dollars $\sigma_Y =$ ______ dollars

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Problem 1165

Find the P-value for the indicated hypothesis test with the given standardized test statistic, $z$ . Decide whether to reject $H_0$ for the given level of significance $\alpha$ . Right-tailed test with test statistic $z = 1.39$ and $\alpha = 0.04$ . P-value = (Round to four decimal places as needed.)

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Problem 1166

Which of the following are characteristics of a normal distribution? The normal distribution curve crosses the $x$ axis. The normal distribution curve is symmetric about the standard deviation. The total area under the normal distribution curve is 1.00 .
The area under the part of a normal curve that lies within 3 standard deviations of the mean is approximately 0.95 . The area under the part of a normal curve that lies within 1 standard deviation of the mean is approximately 0.68 . The normal distribution curve is unimodal. A normal distribution curve is bell shaped. The mean, median, and mode are located at the center of the distribution. The normal curve is a discrete distribution.
The area under the part of a normal curve that lies within 2 standard deviations of the mean is approximately 0.95 . Check

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Problem 1167

12. A random sample of 110 lightning flashes in a certain region resulted in a sample average radar echo duration of $0.81$ sec and a sample standard deviation of $0.34$ sec ("Lightning Strikes to an Airplane in a Thunderstorm," J. of Aircraft, 1984: 607-611). Calculate a 99% (two-sided) confidence interval for the true average echo duration $\mu$ , and interpret the resulting interval.

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Problem 1168

13. The article "Extravisual Damage Detection: Defining the Standard Normal Tree" (Photogrammetric Engr. and Remote Sensing, 1981: 515-522) discusses there use of color infrared photography in identification of normal trees in Douglas fir stands. Among data reported were summary statistics for green-filter analytic optical densitometric measurements on samples of both healthy and diseased trees. For a sample of 69 healthy trees, the sample mean dye-layer density was 1.028, and the sample standard deviation was 0.163. a. Calculate a $95\%$ (two-sided) CI for the true average dye-layer density for all such trees. b. Suppose the investigators had made a rough guess of 0.16 for the value of $s$ before collecting late a $95\%$ (two-sided) confidence interval for the proportion of all dies that pass the probe.

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Problem 1169

A potato chip manufacturer produces bags of potato chips that are supposed to have a net weight of 326 grams. Because the chips vary in size, it is difficult to fill the bags to the exact weight desired. However, the bags pass inspection so long as the standard deviation of their weights is no more than 4 grams. A quality control inspector wished to test the claim that one batch of bags has a standard deviation of more than 4 grams, and thus does not pass inspection. If a sample of 28 bags of potato chips is taken and the standard deviation is found to be 4.6 grams, does this evidence, at the 0.025 level of significance, support the claim that the bags should fail inspection? Assume that the weights of the bags of potato chips are normally distributed.
Step 3 of 3: Draw a conclusion and interpret the decision.
Answer 2 Points Tables Keypad Keyboard Shortcuts
We reject the null hypothesis and conclude that there is sufficient evidence at a 0.025 level of significance that the bags should fail inspection.
We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.025 level of significance that the bags should fail inspection.
We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.025 level of significance that the bags should fail inspection.
We reject the null hypothesis and conclude that there is insufficient evidence at a 0.025 level of significance that the bags should fail inspection.

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Problem 1170

Assume that a procedure yields a binomial distribution with a trial repeated $n=30$ times. Use the binomial probability formula to find the probability of $x=5$ successes given the probability $p='15$ of success on a single trial. Round to three decimal places.

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Problem 1171

John collects the running times of some athletes and records the data in the table below. \begin{tabular}{|c|c|} \hline Time $(z$ seconds) & Frequency \\ \hline $50<z \leq 60$ & 7 \\ \hline $60<z \leq 70$ & 4 \\ \hline $70<z \leq 80$ & 3 \\ \hline $80<z \leq 90$ & 7 \\ \hline \end{tabular}
Find the mean of the data in the table. Give your answer correct to 1 decimal place where appropriate.

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Problem 1172

5.12: Let the random variable $Y_n$ have distribution that is $b(n, p)$ a) Prove that $\frac{X_n}{n}$ converges in probability to $p$ . This result is one form of the weak law of large numbers. b) Prove that $1 - \frac{X_n}{n}$ converges in probability to $1 - p$ c) Prove that $(\frac{X_n}{n})(1 - \frac{Y_n}{n})$ converges in probability to $p(1 - p)$

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Problem 1173

The weights of badgermoles in the Earth Kingdom are normally distributed, with mean weight 1150 kg and standard deviation 50 kg . Find the probability that a badgermole caught at random has a weight greater than 1260 kg . z Table Link 0.0122 0.0162 0.0158 0.0150

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Problem 1174

3. Tricia surveys students in her computer class about time spent on computers by students in her school. Will the survey results from this sample support a valid inference? Explain.

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Problem 1175

A recent poll asked respondents to fill in the blank to this question: "The country $\qquad$ when it comes to giving equal rights to women" with one of three choices. The results are shown in the accompanying table using a sample size of 80 men and 80 women. Complete parts a and b below. \begin{tabular}{|l|c|c|c|c|} \hline & \begin{tabular}{c} Hasn't Gone \\ Far Enough \end{tabular} & \begin{tabular}{c} Has Been \\ About Right \end{tabular} & \begin{tabular}{c} Has Gone \\ Too Far \end{tabular} & Total \\ \hline Men & 33 & 35 & 12 & 80 \\ \hline Women & 43 & 29 & 8 & 80 \\ \hline Total & 76 & 64 & 20 & 160 \\ \hline \end{tabular} A. P(male and responded "hasn't gone far enough") B. P(hasn't gone far enough | male) C. $P$ (male I hasn't gone far enough) b. Find the probability that a person randomly selected from only the men in this group responded "hasn't gone far enough."
The probability is $\square$ (Simplify your answer.)

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Problem 1176

A variable $\boldsymbol{x}$ is normally distributed with mean 25 and standard deviation 3. Round your answers to the nearest hundredth as needed. a) Determine the $z$ -score for $x=28$ . $z=$ $\square$ b) Determine the $z$ -score for $x=20$ . $z=$ $\square$ c) What value of $x$ has a $z$ -score of 1.33 ? $x=$ $\square$ d) What value of $x$ has a $z$ -score of 0.3 ? $x=$ $\square$ e) What value of $x$ has a $z$ -score of 0 ? $x=$ $\square$

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Problem 1177

The lengths of mature trout in a local lake are approximately normally distributed with a mean of $\mu=13.7$ inches, and a standard deviation of $\sigma=1.6$ inches.
Fill in the indicated boxes.
Find the z -score corresponding to a fish that is $\mathbf{1 3 . 3}$ inches long. Round your answer to the nearest hundredth as needed. $z=$ $\square$ How long is a fish that has a z -score of 0.2 ? Round your answer to the nearest tenth as needed. $\square$ inches

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Problem 1178

Mary rolled a cube 40 times. Find the experimental probability of rolling a 4, the theoretical probability, and a true statement.

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Problem 1179

According to a study on teenage shopping behavior, it was found that $75\%$ of female teens regularly shop in stores rather than shopping online. If a group of 6 female teenagers are selected at random, what is the probability that at least 3 of them regularly do their shopping in stores? (Round your answer to four decimal places.)

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Problem 1180

h. Interpret the level of significance in the context of the study. - There is a $10 \%$ chance that there is a difference in the proportion of blonde and brunette college students who have a boyfriend. If the percent of all blonde college students who have a boyfriend is the same as the percent of all brunette college students who have a boyfriend and if another 638 blonde college students and 791 brunette college students are surveyed then there would be a $10 \%$ chance that we would end up falsely concuding that the population proportion of blonde college students who have a boyfriend is greater than the population proportion of brunette college students who have a boyfriend If the percent of all blonde college students who have a boyfriend is the same as the percent of all brunette college students who have a boyfriend and if another 638 blonde college students and 791 brunette college students are surveyed then there would be a $10 \%$ chance that we would end up falsely concuding that the proportion of these surveyed blonde and brunette college students who have a boyfriend differ from each other. There is a $10 \%$ chance that you will never get a boyfriend unless you dye your hair blonde.

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Problem 1181

Do men score higher on average compared to women on their statistics finals? Final exam scores of thirteen randomly selected male statistics students and twelve randomly selected female statistics students are shown below.
Male: $\begin{array}{lllllllllllll}93 & 77 & 64 & 71 & 72 & 62 & 84 & 70 & 89 & 73 & 63 & 88 & 94\end{array}$ $\begin{array}{lllllllllllll}\text { Female: } 83 & 46 & 58 & 81 & 49 & 74 & 62 & 70 & 69 & 66 & 58 & 68\end{array}$ Assume both follow a Normal distribution. What can be concluded at the the $\alpha=0.01$ level of significance level of significance?
For this study, we should use Select an answer a. The null and alternative hypotheses would be: $H_{0}$ : Select an answer Select an answer Select an answer (6) (please enter a decimal) $H_{1}$ : Select an answer Select an answer Select an answer (Please enter a decimal) b. The test statistic ? $0=$ $\square$ (please show your answer to 3 decimal places.) c. The $p$ -value $=$ $\square$ (Please show your answer to 4 decimal places.) d. The $p$ -value is ? $\alpha$ e. Based on this, we should Select an answer the null hypothesis. f. Thus, the final conclusion is that ... The results are statistically insignificant at $\alpha=0.01$ , so there is statistically significant evidence to conclude that the population mean statistics final exam score for men is equal to the population mean statistics final exam score for women. The results are statistically significant at $\alpha=0.01$ , so there is sufficient evidence to conclude that the population mean statistics final exam score for men is more than the population mean statistics final exam score for women. The results are statistically significant at $\alpha=0.01$ , so there is sufficient evidence to conclude that the mean final exam score for the thirteen men that were observed is more than the mean final exam score for the twelve women that were observed. The results are statistically insignificant at $\alpha=0.01$ , so there is insufficient evidence to conclude that the population mean statistics final exam score for men is more than the population mean statistics final exam score for women.

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Problem 1182

Let $y$ denote the number of broken eggs in a randomly selected carton of one dozen eggs. \begin{tabular}{|c|c|c|c|c|c|} \hline $y$ & 0 & 1 & 2 & 3 & 4 \\ \hline $p(y)$ & 0.60 & 0.25 & 0.10 & 0.03 & 0.02 \\ \hline \end{tabular} (a) Calculate and interpret $\mu_{y}$ . $\mu_{y}=$ $\square$ (b) Consider the following questions. (i) In the long run, for what percentage of cartons is the number of broken eggs less than $\mu_{y}$ ? $\qquad$ \% (ii) Does this surprise you? Yes No (c) Explain why $\mu_{y}$ is not equal to $\frac{0+1+2+3+4}{5}=2.0$ . This computation of the mean is incorrect because it does not take into account that the number of broken eggs are all equally likely. This computation of the mean is incorrect because the value in the denominator should equal the maximum $y$ value. This computation of the mean is incorrect because it does not take into account the number of partially broken eggs. This computation of the mean is incorrect because it includes zero in the numerator which should not be taken into account when calculating the mean. This computation of the mean is incorrect because it does not take into account the probabilities with which the number of broken eggs need to be weighted.

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Problem 1183

1 2 $=3$ $\checkmark 4$ 6 7 5 8 9 10
High Blood Pressure Twenty-one percent of Americans ages 25 to 74 have high blood pressure. If 16 randomly selected Americans ages 25 to 74 are selected, find each probability. Round your answers to at least 3 decimal places.
Part 1 of 3 (a) None will have high blood pressure. $P($ none have high blood pressure $)=0.025$
Part 2 of 3 (b) One-half will have high blood pressure. $P$ (one-half have high blood pressure) $=0.007$
Part: $2 / 3$
Part 3 of 3 (c) Exactly 7 will have high blood pressure. $P($ exactly 7 have high blood pressure $)=$ $\square$

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Problem 1184

Question 4
Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the height of a man with a $z$ -score of 0.3571 (to 4 decimal places) $\square$

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Problem 1185

Question 6
In a large population, $55 \%$ of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
Give your answer as a decimal to 4 places.

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Problem 1186

Question 13
In a recent poll, 580 people were asked if they liked dogs, and 68\% said they did. Find the Margin of Error for this poll, at the $99 \%$ confidence level. Give your answer to four decimal places if possible. $\square$

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Problem 1187

Aisha wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 77 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 7.1 and a standard deviation of 1.7. What is the $80 \%$ confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Assume the data is from a normally distributed population. Round answers to 3 decimal places where possible. $\square$ $<\mu<$ $\square$

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Problem 1188

\begin{tabular}{cccc} & Bachelor's & Master's & Doctorate \\ Men & 653,037 & 313,838 & 25,771 \\ Women & 687,564 & 315,906 & 25,253 \end{tabular}
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Choose a degree at random. Find the probabilities of the following. Express your answer as a fraction or a decimal rounded to three decimal places.
Part 1 of 4 (a) What is the probability that the degree is a bachelor's degree? $P(\text { bachelor's degree })=0.663$
Part 2 of 4 (b) What is the probability that the degree was a master's degree or a degree awarded to a women? $P(\text { master's degree or awarded to woman })=0.664$
Part: 2 / 4
Part 3 of 4 (c) What is the probability that the degree was a bachelor's degree awarded to a men. $P(\text { bachelor's degree awarded to men })=$ $\square$ Skip Part Check Save For Later Submit Assianm

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Problem 1189

\begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{\begin{tabular}{c} At a basketball game, you ask random students what \\ his or her favorite movie gener is to determine the \\ schools favorite type of movie. \end{tabular}} \\ \hline Population & $$ \\ \hline Sample & $$ \\ \hline What is biased? & $*$ \\ \hline \begin{tabular}{c} How can it be \\ fixed? \end{tabular} & \\ \hline \end{tabular}

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Problem 1190

Question 14 of 25 (1 point) | Question Attempt: 1 or I
College Degrees Awarded The table below represents the college degrees awarded in a recent academic year by Español gender. \begin{tabular}{cccc} & Bachelor's & Master's & Doctorate \\ \hline Men & 548,254 & 251,468 & 23,728 \\ Women & 609,872 & 270,538 & 23,320 \end{tabular} Send data to Excel
Choose a degree at random. Find the probabilities of the following. Express your answer as a fraction or a decimal rounded to three decimal places.
Part: $0 / 4$ $\square$
Part 1 of 4 (a) What is the probability that the degree is a doctorate? $P(\text { doctorate })=0.027$ $\square$
Part: $1 / 4$ $\square$
Part 2 of 4 (b) What is the probability that the degree was a bachelor's degree or a degree awarded to a men? $P(\text { bachelor's degree or awarded to men })=$ $\square$ Next Part

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Problem 1191

Suppose $X \sim N(2, 6)$ . What value of $x$ has a $z$ -score of three?

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Problem 1192

From historical data, $18 \%$ of people work out daily $(p=0.18)$ . In a sample of 15 $(n=15)$ people, use the binomial formula or your TI-8314 to determine the probability that exactly 4 (of the fifteen) work out daily.
For a standard normal distribution: a) What is the probability that $z$ is less than 0.47 ? b) What is the probability that $z$ is greater than -1.83 ? $\qquad$ c) What is the probability that $z$ is between -1.29 and 0.64 ? $\qquad$ d) What is the probability that $z$ is between -1.96 and 1.96 ? $\qquad$

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Problem 1193

For a population with $\mu = 100$ and $\sigma = 20$ , what is the $X$ value corresponding to $z = 0.25$ ? 90 110 105 95 Need Help? Read It

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Problem 1194

An aptitude test is designed to measure leadership abilities of the test subjects. Suppose that the scores on the test are normally distributed with a mean of 570 and a standard deviation of 120. The individuals who exceed 700 on this test are considered to be potential leaders. What proportion of the population are considered to be potential leaders? Round your answer to at least four decimal places. $\square$

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Problem 1195

$\checkmark 1$ $\checkmark 2$ $\checkmark 3$ $\checkmark 4$ $\checkmark 5$ 6 $\times 7$ 8 9 10
Caffeine in Tea Bags In a recent study, researchers found that the average amount of caffeine in tea bags is 26 mg . The standard deviation of the population is 3 mg . If a random sample of 46 newly manufactured tea bags has a mean of 25.1 mg of caffeine, can it be concluded that the new brand of tea bags contain less caffeine than the average found in the recent study? Use $\alpha=0.05$ , and use the $P$ -value method with tables.
Part: $0 / 5$
Part 1 of 5 (a) State the hypotheses and identify the claim. $\begin{array}{l} H_{0}: \square \text { (Choose one) } \nabla \\ H_{1}: \square \text { claim } \\ \text { not claim } \end{array}$

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Problem 1196

A political newspaper, Keeping It Political, is interested in the distances voters in Vanville County live from their nearest polling station. Keeping It Political has hired you to estimate the population mean of all such distances for voters in this county. To estimate this population mean, you select a random sample of 23 Vanville County voters and record the distance (in km ) each voter lives from their nearest polling station. Assume the population is approximately normally distributed. Based on your sample, follow the steps below to construct a $95 \%$ confidence interval for the population mean of all the distances voters in Vanville County live from their nearest polling station. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results for your random sample. \begin{tabular}{|c|c|c|} \hline Number of voters & Sample mean & \begin{tabular}{c} Sample standard \\ deviation \end{tabular} \\ \hline 23 & 4.192 & 2.041 \\ \hline \end{tabular}
Enter the values of the sample size, the point estimate of the mean, the sample standard deviation, and the critical value you need for your $95 \%$ confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute". \begin{tabular}{|l|l|} \hline Sample size: \\ $\square$ \end{tabular} \begin{tabular}{|c|l|} \hline \begin{tabular}{c} Confidence \\ level \end{tabular} & Critical value \\ \hline $99 \%$ & $t_{0.005}=2.819$ \\ \hline $95 \%$ & $t_{0.025}=2.074$ \\ \hline $90 \%$ & $t_{0.050}=1.717$ \\ \hline \end{tabular}

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Problem 1197

The following table shows the distribution of murders by type of weapon for murder cases in a particular country over the past 12 years. Complete Weapon parts (a) through (e).
Weapon | Probability ------- | -------- Handgun | 0.479 Rifle | 0.026 Shotgun | 0.033 Unknown firearm | 0.148 Knives | 0.135 Hands, fists, etc. | 0.054 Other | 0.125
(a) Is the given table a probability model? Why or why not? A. No; the probability of all events in the table is not greater than or equal to 0 and less than or equal to 1, and the sum of the probabilities of all outcomes does not equal 1. B. No; the sum of the probabilities of all outcomes does not equal 1. C. No; the probability of all events in the table is not greater than or equal to 0 and less than or equal to 1. D. Yes; the rules required for a probability model are both met.
(b) What is the probability that a randomly selected murder resulted from a rifle or shotgun? $P(\text{rifle or shotgun}) =$ (Type a decimal rounded to three decimal places as needed.)

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Problem 1198

Railroad Crossing Accidents The data show the number of railroad crossing accidents for the 50 states of the United States for a specific year. \begin{tabular}{cc} Class limits & Frequency \\ \hline $1-43$ & 25 \\ $44-86$ & 17 \\ $87-129$ & 1 \\ $130-172$ & 2 \\ $173-215$ & 0 \\ $216-258$ & 1 \\ $259-301$ & 3 \\ $302-344$ & 1 \\ \cline { 2 - 2 } & Total 50 \end{tabular} Send data to Excel
Construct a histogram for the data using relative frequencies. Round values to two decimal places. Railroad Crossing Accidents

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Problem 1199

Homework: HW \#7: Sections 6.1-6.3 Question 9, 6.1.21-T HW Score: $16.67 \%, 8$ of 48 points Part 1 of 2 Points: 0 of 1 Save
Question list Question 9 Question 10 Question 11 Question 12 Question 13 Question 14
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1 . Draw a graph and find the probability of a bone density test score greater than 0.59 . $\qquad$ Sketch the region. Choose the correct graph below. A. B. c.
D. Help me solve this View an example Get more help - Clear all Check answer Dec 9 2:36 US

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Problem 1200

She repeats this several times. The table shows her results.
Based on her results, what is the probability of choosing an orange marble from the bag?
Color Frequency Green 5 Orange 11 Purple 4
Color Probability Green $\frac{1}{4}$ Orange

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1 ...9 10 11 12 13 14

Distribution

Problem 1101

Problem 1102

Find the probability that a randomly chosen American has type B blood, given that 15%15\%15% of Americans have type B.

Problem 1103

Is a score of X=70X=70X=70 extreme for a population with mean μ=50\mu=50μ=50 and σ=20\sigma=20σ=20? How about with σ=5\sigma=5σ=5?

Problem 1104

Find the probability that a random American has type B blood (15%15\%15%) and the probability of having type A or B.

Problem 1105

Find the probability of randomly selecting a school with 100 or fewer computers. Round to 3 decimal places.

Problem 1106

In 2002, the median home price was \$ 184,200. Which standard deviation is most plausible: \$ 2000, \$ 60,000, or \$ 1,000,000? Why?

Problem 1107

For 57 female athletes, xˉ=72.4\bar{x}=72.4xˉ=72.4 and s=13.6s=13.6s=13.6. Use the empirical rule to find the interval for 68%68\%68% of data.

Problem 1108

Data from 57 female athletes shows xˉ=72.4\bar{x}=72.4xˉ=72.4 and s=13.6s=13.6s=13.6. Use the empirical rule to find intervals for 68% and 95%.

Problem 1109

For 57 female athletes, xˉ=72.4\bar{x}=72.4xˉ=72.4 and s=13.6s=13.6s=13.6. Use the empirical rule to find intervals for 68%, 95%, and nearly all data.

Problem 1110

What is the probability that Ava is assigned the numbers 1, 5, or 10 out of 16 possible tryout numbers?

Problem 1111

Find the percentage of scores between 158 and 872872872 in a normal distribution with mean 515 and std dev 119.

Problem 1112

A standardized test's math scores have a mean of 515 and a standard deviation of 119. Find the percentages for the given ranges.

Problem 1113

A standardized test has scores with a mean of 515 and a standard deviation of 119. Find the percentages for parts (a), (b), and (c).

Problem 1114

Find nnn and ΣX\Sigma XΣX for the frequency distribution: xxx: 5-2, 4-2, 3-2, 2-4, 1-1.

Problem 1115

Approximate the median from the given frequency distribution table. Report it as the midpoint of the median class.

Problem 1116

Approximate the median of the given frequency distribution. Report as the midpoint of the median class.

Problem 1117

Approximate the median from the given frequency distribution table. Report the midpoint of the median class.

Problem 1118

What is the minimum number of prizes, all powers of 2, needed to total \$ 988?

Problem 1119

Determine the expected shape of the histogram for student scores (out of 100) on a difficult exam: symmetric, skewed right, or skewed left?

Problem 1120

For 57 female athletes, xˉ=74.8\bar{x}=74.8xˉ=74.8 and s=13.8s=13.8s=13.8. Use the empirical rule to find the intervals for 68%, 95%, and nearly all data.

Problem 1121

Identify the type of distribution: right tail longer than left tail. Options: skewed right, symmetric, skewed left, not skewed, none.

Problem 1122

Given data for 57 female athletes shows xˉ=86.1\bar{x}=86.1xˉ=86.1 and s=13.3s=13.3s=13.3. Use the empirical rule to find intervals for 68%, 95%, and nearly all.

Problem 1123

Problem 1124

Problem 1125

Problem 1126

Problem 1127

Problem 1128

Problem 1129

Problem 1130

Avg 28 Stdev 3 What 2 values will 95\% of days be

Problem 1131

Avg 28 Stdev 3 What 2 values will 95% of days be

Problem 1132

Find the critical value For confidence level of 98%98\%98%

Problem 1133

Problem 1134

Problem 1135

A simple random sample of size 35 has mean x=3.49x = 3.49x=3.49. The population standard deviation is σ=1.59\sigma = 1.59σ=1.59. Construct a 90% confidence interval for the population mean.The parameter is the population mean.The correct method to find the confidence interval is the ttt method.

Problem 1136

If XXX is a binomial random variable with nnn trials and success probability ppp, then as nnn gets larger, the distribution of XXX becomes (Choose one) skewed, less

Problem 1137

Assume the variable XXX is normally distributed with mean 120 and standard deviation 13. Find P(100<X<155)P(100 < X < 155)P(100<X<155) NOTE: You must add an attachment to this question that shows all of your work in getting the answer to receive credit.

Problem 1138

Use the Cumulative Normal Distribution Table to find the zzz-score for which the area to its left is 0.690.690.69. The zzz-score for the given area is

Problem 1139

(a) The following dotplot illustrates a sample. The dotplot reveals (Choose one) approximately norman outlier a large degree of skewness more than one distinct mode none of these features Therefore, we (Choose one)

Problem 1140

(d) The following stem-and-leaf plot illustrates a sample. 4|6 5|5 6|2 7| 8|17 9|2445 10|011245569 11|58 The stem-and-leaf plot reveals (Choose one) from an approximately normal population. Therefore, we (Choose one)

Problem 1141

xxx | P(x)P(x)P(x) ---|--- 56 | 0.3 66 | 0.8 76 | 0.2 86 | -0.3 Determine whether the table represents a discrete probability distribution. Explain why The table (Choose one) represent Send data to Excel

Problem 1142

Problem 1143

Problem 1144

Determine whether the distribution represents a probability distribution.XXX | 3 | 7 | 10 P(X)P(X)P(X) | 0.1 | 0.3 | -0.2Send data to ExcelPart: 0 / 2Part 1 of 2The distribution (Choose one) a probability distribution. represents does not represent

Problem 1145

Problem 1146

Problem 1147

Find the probability that a randomly chosen American has type B blood, given that $15\%$ of Americans have type B.

Is a score of $X=70$ extreme for a population with mean $\mu=50$ and $\sigma=20$ ? How about with $\sigma=5$ ?

Find the probability that a random American has type B blood ( $15\%$ ) and the probability of having type A or B.

For 57 female athletes, $\bar{x}=72.4$ and $s=13.6$ . Use the empirical rule to find the interval for $68\%$ of data.

Data from 57 female athletes shows $\bar{x}=72.4$ and $s=13.6$ . Use the empirical rule to find intervals for 68% and 95%.

For 57 female athletes, $\bar{x}=72.4$ and $s=13.6$ . Use the empirical rule to find intervals for 68%, 95%, and nearly all data.

Find the percentage of scores between 158 and $872$ in a normal distribution with mean 515 and std dev 119.

Find $n$ and $\Sigma X$ for the frequency distribution: $x$ : 5-2, 4-2, 3-2, 2-4, 1-1.

For 57 female athletes, $\bar{x}=74.8$ and $s=13.8$ . Use the empirical rule to find the intervals for 68%, 95%, and nearly all data.

Given data for 57 female athletes shows $\bar{x}=86.1$ and $s=13.3$ . Use the empirical rule to find intervals for 68%, 95%, and nearly all.

Find the critical value For confidence level of $98\%$

A simple random sample of size 35 has mean $x = 3.49$ . The population standard deviation is $\sigma = 1.59$ . Construct a 90% confidence interval for the population mean.
The parameter is the population mean.
The correct method to find the confidence interval is the $t$ method.

If $X$ is a binomial random variable with $n$ trials and success probability $p$ , then as $n$ gets larger, the distribution of $X$ becomes (Choose one) skewed, less

Assume the variable $X$ is normally distributed with mean 120 and standard deviation 13. Find $P(100 < X < 155)$ NOTE: You must add an attachment to this question that shows all of your work in getting the answer to receive credit.

Use the Cumulative Normal Distribution Table to find the $z$ -score for which the area to its left is $0.69$ . The $z$ -score for the given area is

$x$ | $P(x)$ ---|--- 56 | 0.3 66 | 0.8 76 | 0.2 86 | -0.3 Determine whether the table represents a discrete probability distribution. Explain why The table (Choose one) represent Send data to Excel

Determine whether the distribution represents a probability distribution.
$X$ | 3 | 7 | 10 $P(X)$ | 0.1 | 0.3 | -0.2
Send data to Excel
Part: 0 / 2
Part 1 of 2
The distribution (Choose one) a probability distribution. represents does not represent

12. When four fair coins are tossed, what is the probability that the outcome will consist of two heads and two tails? (A) $\frac{1}{2}$ (B) $\frac{11}{20}$ (C) $\frac{1}{3}$ (D) $\frac{1}{4}$ (E) $\frac{3}{8}$

Data from a book fair shows the number of books bought by 20 youths. Find the mean, standard deviation, and $70^{\text{th}}$ percentile.

Find the percentage of values below $125$ in a normal distribution with mean $159$ and standard deviation $17$ .

$n = 28$ , $p = 0.55$ Mean: $\mu =$ Variance: $\sigma^2 =$ Standard deviation: $\sigma =$ Part 3 of 4

Assume that a procedure yields a binomial distribution with a trial repeated $n=30$ times. Use the binomial probability formula to find the probability of $x=5$ successes given the probability $p='15$ of success on a single trial. Round to three decimal places.