Browse Statistics problems in the Studdy Learning Bank!

Problem 101

Which score has the highest relative position given the mean $\bar{X}$ and standard deviation $s$ ?

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Problem 102

Find the mean of the discrete distribution with $X = \{4, 6\}$ and $P(X) = \{0.51, 0.49\}$ .

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Problem 103

Find the range (difference between largest and smallest values) of the data $[101, 521, 125, 325, 107, 125, 917]$ .

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Problem 104

Determine if the mean FICO credit score is greater than 720 using a sample of 50 people with mean 765 and standard deviation 98. Use $\alpha=0.01$ level of significance and the P-value method.
$\begin{array}{l} H_0: \mu \leq 720 \\ H_1: \mu > 720 \end{array}$
This hypothesis test is a right-tailed test.

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Problem 105

Determine if two independent samples from normal populations have equal means using a two-tailed test at $\alpha = 0.05$ . The test statistic is $t = -1.67$ , and the p-value is $\square$ .

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Problem 106

Valve regulates water pressure on 180 engines. Mean pressure is 6.2 lbs/square inch, variance is 0.25. Determine if there is sufficient evidence at 0.02 level that valve does not meet 6.3 lbs/square inch specification.
$H_0$ : $\mu = 6.3$ lbs/square inch $H_a$ : $\mu \neq 6.3$ lbs/square inch

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Problem 107

Calculate the range of the data set with $n=10$ observations: $\text{range} = \max(63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9) - \min(63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9)$ .

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Problem 108

Find the p-value for a two-tailed test with test statistic $z=-1.225$ to determine if the proportion of men over 50 who regularly have their prostate examined is significantly different from 0.16.

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Problem 109

Fill in the blank: A histogram aids in analyzing the $\text{shape of the distribution}$ of the data.

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Problem 110

A new film received a median rating of $7.23$ stars. The first and third quartiles are $2.78$ and $8.24$ stars, respectively. What is the most likely statement?

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Problem 111

Find the percentage of bolts with diameter > $0.32$ inches, given the bolt diameters are normally distributed with mean $0.30$ inches and standard deviation $0.01$ inches. Round to 2 decimal places.

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Problem 112

Find the most common birth weight among 8 babies with weights $4, 5, 5, 3, 5, 4, 5, 4$ kg.

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Problem 113

Find the range of time taken by students on a recent exam, given a bell-shaped distribution with $\mu = 45.3$ minutes and $\sigma = 5.6$ minutes, using the range rule of thumb.

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Problem 114

Determine the set of data represented by the given stem-and-leaf plot: $7 \, 3, 4, 5; \, 6 \, 2, 7; \, 5 \, 1, 3, 4$

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Problem 115

Find the probability $P(Z > -0.93)$ for the standard normal variable $Z$ . Round the answer to at least three decimal places.

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Problem 116

Identify outliers among the 11 sandwich calorie values: $593, 594, 595, 596, 599, 602, 604, 604, 605, 606, 607$ .

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Problem 117

Select the appropriate term to describe the information collected about individuals. The characteristics are called $\mathbf{variables}$ .

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Problem 118

Calculate the standard deviation of the given data: $x = \{-8, -7, -6, -5, -4, -3\}$ and $P(X=x) = \{0.1, 0.1, 0.2, 0.1, 0.3, 0.2\}$ . Round the answer to one decimal place.

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Problem 119

Find the average of the numbers $62, 61, 46, 61, 50$ and round the result to the nearest tenth.

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Problem 120

a. Probability that a consumer who dislikes Crunchicles is 18-24 years old: $\frac{2}{14}$
b. Probability that a randomly selected consumer dislikes Crunchicles: $\frac{14}{300}$
c. Probability that a randomly selected consumer is 35-55 years old or likes Crunchicles: $\frac{3 + 38}{300}$
d. Probability that a 70-year-old consumer likes Crunchicles: $\frac{20}{172}$

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Problem 121

Seat belt usage affects deaths. For every 1% increase in usage, deaths decrease by 280. Find the slope $b$ and predict deaths if (i) 0%, (ii) 74%, (iii) 100% wear seat belts, given $y$ -intercept is 28,910.
a. The slope is $b = -280$ .

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Problem 122

Find the average length of the fish in the tank: $2, 3, 1, 4, 5, 2, 2$ . Round the mean to the nearest tenth.

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Problem 123

Given a stem-and-leaf plot, find the mean, median, mode, and sample size of the distribution. $300.6, 231.5, 135.0, 10$ or $271, 217, 272, 5$ or $32, 32, 35, 10$ or $18.2, 20, 20, 5$ .

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Problem 124

Claim that the standard deviation of adult male pulse rates is less than 10 beats/min. For a sample of 138 males, the standard deviation is $8.5$ beats/min. Find the test statistic.

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Problem 125

Berechne Mittelwert, Median und Quartilsabstand für die Datenreihe: $3 ; 8 ; 12 ; 5 ; 7 ; 8 ; 9,5 ; 11 ; 14 ; 6 ; 8,5$ .

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Problem 126

Evaluate the formula $E=z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$ for given values of $z$ , $\hat{p}$ , and $n$ . Round the result to three decimal places.

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Problem 127

Find the percentage of people with IQ scores between $88$ and $116$ in a normal distribution with $\mu=100$ and $\sigma=15$ , rounded to the nearest tenth.

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Problem 128

Find power function $y=a \times b^x$ and linear function $y=mx+c$ to model data set $(x, y)$ . Power function coefficients $a=4.287$ , $b=1.204$ . Determine which function better fits the data.

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Problem 129

Find the best predicted IQ score $\hat{y}$ for a wife given her husband's IQ of $97$ , using a significance level of $0.05$ , where $\bar{x}=101.08$ , $\bar{y}=101.25$ , $r=0.825$ , and $\hat{y}=10.2+0.9x$ .

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Problem 130

For a survey of 18-year-old males, find the weights representing the 99th, 43rd, and first quartile percentiles given a mean of $167.5$ pounds and a standard deviation of $48.6$ pounds.

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Problem 131

Find the r-value with the strongest negative correlation: $-0.9$ , $-0.6$ , $-0.7$ , or $-0.8$ .

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Problem 132

Find the probability that two randomly selected drive-thru orders are both accurate given the data in the table. Assume the selections are made with replacement. Determine if the events are independent.
a. The probability is $\frac{(336 \times 260)}{(336 + 33) \times (260 + 50)}$ . The events are independent.

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Problem 133

Find the percentile for the data value $125$ in the given set: $119, 131, 123, 117, 125, 127, 117, 115, 122, 119, 123, 133, 115, 119, 121, 116$ .

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Problem 134

Analyze the trend in women's finishers at the NYC Marathon from 1997 to 2001 using a scatter plot and describe any relationship.

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Problem 135

In a survey of 254 students, $86\%$ enjoyed their classes. Find the margin of error, rounded to the nearest tenth of a percent.

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Problem 136

Find the degrees of freedom for the given t-interval: $\bar{x}=17.598$ , $s_x=16.01712719$ , $n=50$ .

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Problem 137

Estimate the proportion of first-time customers from a sample of 129 orders, given that 36% of orders come from first-time customers. Find the probability that the sample proportion is between 0.29 and 0.41.

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Problem 138

Find a 99% confidence interval for the true mean lifetime of a brand of light bulbs with a sample of 80 bulbs having a mean lifetime of $497$ hours and a standard deviation of $45$ hours. The lower and upper limits are $488.5$ and $505.5$ hours, respectively.

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Problem 139

The median ticket price for musicals is $95 and for non-musical plays is$ 80. Calculate the difference in median ticket costs between musicals and non-musical plays.

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Problem 140

Find the class with the highest average and least score variability from $\{A, B, C, D\}$ where each class has a range of $\{56, 55, 48, 57\}$ and mean scores $\{107, 114, 108, 105\}$ .

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Problem 141

A college admissions officer takes a random sample of 100 entering freshmen and finds their mean mathematics SAT score is 436. Assuming the population standard deviation is $\sigma=115$ , construct a $99\%$ confidence interval for the mean mathematics SAT score of the entering freshman class, rounded to the nearest whole number.
A $99\%$ confidence interval for the mean mathematics SAT score is $\boxed{395}<\mu<\boxed{477}$ .

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Problem 142

Find the range of the values in the table, where $X = \{-1, 3, 3, 4\}$ and $Y = \{-2, 0, -2, 5\}$ .

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Problem 143

Determine the probability a person aged 46+ prefers cash payment from the given data.
$P(\text{Cash} | \text{Age } 46+) = \frac{35}{35 + 25}$

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Problem 144

Test claim that sample from population with mean < 1000 hic (head injury condition units) using 0.01 significance level. Hypotheses: $H_0: \mu = 1000$ hic, $H_1: \mu < 1000$ hic. Test statistic $t = \square$ (rounded to 3 decimal places). $P$ -value = $\square$ (rounded to 4 decimal places). Conclude $H_0$ is rejected, evidence supports claim that sample is from population with mean < 1000 hic. Results suggest most booster seats meet requirement, but one may exceed 1000 hic.

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Problem 145

Draw a histogram for the lengths of stay (in days) of 19 patients discharged from a hospital, with class boundaries from 1.5 to 13.5 and 6 equal-width classes.

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Problem 146

Create a stem-and-leaf display with $3 \le$ stem values $\le 10$ , $1 \le$ leaf values $\le 100$ , and at least $20$ leaf values between $5$ and $20$ .

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Problem 147

Determine how the median changes when 15 is added to a data set of 5 numbers: [13, 24, 18, 12, 29]. The median can stay the same, decrease by 1.5, or increase by 1.5.

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Problem 148

Determine if consumer product ratings (0-10) have changed from last year to this year. Given a table of 8 consumer ratings, test at $\alpha=0.05$ if there is enough evidence to conclude the ratings have changed, assuming random, dependent samples from a normal population. Calculate $\bar{d}$ , $s_d$ , and t-test statistic t. Decide to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

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Problem 149

Determine if a statistics student's calculated mean $\bar{x}=-10$ is possible.

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Problem 150

Find the average rate of change in public library visits from 1997 ( $1.4$ billion) to 2001 ( $1.5$ billion). The average rate of change was $0.025$ billion per year.

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Problem 151

Find the modes of the data set $5, 6, 4, 4, 4, 3, 7, 3, 3, 7, 7$ . If there is more than one mode, write them separated by commas. If there is no mode, click on "No mode."

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Problem 152

Complete a table for 5 graph values. Given mean of 5, calculate distance of each score $X=1, X=6, x=7, x=7, x=8$ from the mean.

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Problem 153

To find the degrees for the C region of the pie chart, calculate the percentage of students who got a C, then multiply by 360 degrees. Given: 123 students got a C out of a total of 59 + 84 + 123 + 84 + 62 = 412 students. The percentage of C students is 123/412 = 0.2981, which rounds to 30 degrees.

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Problem 154

Determine the meaning of the constant 378 in the equation $n=-38 g+378$ that models the number of students $n$ in grade $g$ at an elementary school.

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Problem 155

Approximately what percentage of 1-mile Pennsylvania freeway segments have between 26 and 61 potholes, given a mean of $47$ and standard deviation of $7$ ?

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Problem 156

Airline operations manager wants to survey air passengers to estimate percentage preferring aisle seats. Find sample sizes to be 99% confident within 1.5% of true percentage, given (a) no prior information and (b) 38% prefer aisle seats.
(a) $n = 7372$ (b) $n = 600$

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Problem 157

Claim: More than $4.8\%$ of homes have only a landline phone, no wireless. Find symbolic expression for claim.

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Problem 158

Asthma drug trial: 28 of 275 subjects had headaches. Test if headache rate is less than 12% at 1% significance level.
$z=-0.93$ , $p$ -value $= 0.18$ . The test is right-tailed.

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Problem 159

Estimate the true mean size of a university dance company with 99% confidence, assuming normal distribution. Data: $\{35, 35, 30, 29, 28, 27, 26, 25, 22, 21, 47, 40, 25, 22, 22, 30, 26, 40\}$ .

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Problem 160

Estimate the true proportion of adults who would like to travel to outer space with $93\%$ confidence. Use a graphing calculator and round the answer to at least three decimal places.

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Problem 161

Test if the percentage of blue candies is 23% in a sample of 100 candies. Choose the correct null and alternative hypotheses.
A. $H_0: p \neq 0.23, H_1: p=0.23$ B. $H_0: p=0.23, H_1: p>0.23$ C. $H_0: p=0.23, H_1: p \neq 0.23$ D. $H_0: p=0.23, H_1: p<0.23$

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Problem 162

Estimate the mean height of all female students at a college using a random sample of 36 students. The sample mean is 65.3 inches and the standard deviation is 5.2 inches. Find the $90\%$ confidence interval for the true mean, assuming a normal distribution.

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Problem 163

Test claim about population mean $\mu$ using t-test at $\alpha=0.10$ . Given: $\mu=74, \bar{x}=77.4, s=3.4, n=27$ . What are the null and alternative hypotheses? The correct answer is B: $H_0: \mu=74, H_A: \mu \neq 74$ . The value of the standardized test statistic is $\frac{\bar{x} - \mu}{s/\sqrt{n}} = 5.29$ . (Rounded to two decimal places)

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Problem 164

Estimate the proportion (p) of the voting population that prefers Candidate A, given that 80 out of 100 sampled people preferred A. Use a $99 \%$ confidence level and give the answer as a decimal to three places.

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Problem 165

Find the percentage of $400 \mathrm{~W}$ light bulbs with lifetimes less than 720 hours, given a normal distribution with $\mu = 680$ hours and $\sigma = 125$ hours.

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Problem 166

The hockey team's points per season increase by an average of 3 points, starting with 43.5 points.

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Problem 167

Redefine a problem statement about hypothesis testing for the mean price of existing single-family homes. State the null and alternative hypotheses, and explain the meanings of Type I and Type II errors.
Null hypothesis: Mean price = $243,712. Alternative hypothesis: Mean price ≠$ 243,712. Type I error: Rejecting the null hypothesis when it is true. Type II error: Failing to reject the null hypothesis when it is false.

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Problem 168

Find the probability that a randomly selected 8th grade student in the School of Rock plays the keyboard, expressed as a simplified fraction.
\text{Probability} = \frac{\text{# of 8th grade keyboard players}}{\text{Total # of 8th grade students}}

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Problem 169

Car accident outcomes by seat belt usage: Probability of surviving accident without seat belt is $\frac{165,019}{166,888}$ .

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Problem 170

Find two-sided critical values for a normal distribution at $z_{0.05}$ , $z_{0.025}$ , $z_{0.01}$ , and $z_{0.005}$ given $z_{0.10} = 1.28$ .

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Problem 171

A company claims the mean caffeine content of its 12-oz cola is 40 mg. You test a sample of 30 bottles and find the mean is 37.8 mg. At $\alpha=0.09$ , can you reject the company's claim? Determine the appropriate hypothesis test and critical value(s).

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Problem 172

Construct a scatterplot to show the relationship between protein and carbohydrate content for 12 bean varieties, using carbohydrate content ( $x$ -axis) and protein content ( $y$ -axis).

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Problem 173

Calculate the probabilities of a home pregnancy test given the results: $P($ positive $\mid$ pregnant $)$ , $P($ pregnant $\mid$ positive $)$ , $P($ negative $\mid$ pregnant $)$ , and $P($ not pregnant $\mid$ negative $)$ . Round the answers to the nearest thousandth.

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Problem 174

Find $z$ such that 0.6826 of the area lies between $-z$ and $z$ . Round $z$ to two decimal places.

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Problem 175

Which dataset has the most variation? Compare $95\%$ confidence intervals: $A$ is $1.75$ , $B$ is $6$ , $C$ is $3.4$ . Dataset $B$ has the largest interval, so it has the most variation.

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Problem 176

Find the interval of 400m race times that represent the middle 68% of Easton's normally distributed finishing times with a mean of 80 seconds and standard deviation of 3 seconds.

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Problem 177

Find the area under the standard normal curve to the right of $z=2.7$ . Options: A) 0.0035, B) 0.4965, C) 0.9965

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Problem 178

A patient takes $\$7\$ days to recover from a surgical procedure with a mean recovery time of$ \ $4.9\$ days and a standard deviation of$ \ $2.1\$ days. Find the patient's$ z$-score. (Round to two decimal places.)

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Problem 179

Find the value of $z$ given $x=59$ , $\mu=43$ , and $\sigma=6.2$ . (Round your answer to two decimal places.)

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Problem 180

(a) The most obese countries have obesity rates ranging from $11.4\%$ to $74.6\%$ . Estimate the average obesity percentage. (Round to 2 decimal places)
(b) The US obesity rate is $33.9\%$ . Is this above or below average? above average below average
(c) The US has an obesity rate higher than at least $\%$ of the countries in the data set.

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Problem 181

A virus infects 1 in 400 people. A test is positive 80% if infected and 10% if not infected. Find the probability a person has the virus given a positive test, and the probability a person doesn't have the virus given a negative test, rounded to the nearest tenth of a percent.
$P(A \mid B) = 95.2\%$ $P(A' \mid B') = 99.8\%$

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Problem 182

Find the value of $z$ such that 0.04 of the area lies to the right of $z$ . Round your answer to two decimal places.

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Problem 183

Scatterplot: a graph of paired $(x, y)$ quantitative data that visually shows patterns in the data.

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Problem 184

Fertilized eggs have a mean incubation time of $23$ days and a standard deviation of $1$ day. Find: (a) The $11$ th percentile of incubation times. (b) The incubation times that make up the middle $95\%$ .

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Problem 185

Test if most medical malpractice lawsuits are dropped/dismissed using $H_0: p=0.5$ and $H_1: p>0.5$ at 0.05 significance.

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Problem 186

Find the overall mean height of a class with 13 men (mean 171 cm) and 12 women (mean 165 cm), rounded to two decimal places.
Overall Mean: $\frac{13 \times 171 + 12 \times 165}{13 + 12} \mathrm{~cm}$

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Problem 187

Automobile plant wants to test if mean assembly line completion time $\mu$ has decreased from 44 minutes. With sample mean 42 minutes and population SD 3 minutes:
(a) $H_0: \mu = 44$ , $H_1: \mu < 44$ (b) Not rejecting $H_0$ could be a Type II error. (c) A Type II error would be failing to reject the hypothesis that $\mu$ is 44 minutes when, in fact, $\mu$ is 40 minutes.

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Problem 188

Determine the number of murders per 100,000 residents in states with $9.9$ and $9.7$ thousand automatic weapons, given the model $y=0.87x+3.87$ . Verify the model using linear regression.

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Problem 189

Find the top interval of a frequency table given a set of scores ranging from $X=75$ to $X=23$ , where the bottom interval is $18-23$ .

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Problem 190

If $X=45$ has a 75% percentile rank, determine which statement is true about the score distribution.

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Problem 191

Find the median of the data with given frequencies: $\{1^{1}, 2^{4}, 3^{5}, 4^{4}, 5^{1}, 6^{2}, 7^{4}, 8^{3}\}$ . The median is .

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Problem 192

Find the area under the standard normal curve from 0 to $-2.36$ , the probability a normal random variable falls between 0 and $-2.36$ . Round to 4 decimal places.

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Problem 193

Test whether garlic treatment reduces mean LDL cholesterol level. Null: $\mu \leq 0$ , Alt: $\mu > 0$ . Test statistic: $t = 0.30 / (24.2 / \sqrt{49}) = 0.061$ . P-value: 0.476. The results suggest that garlic treatment is not effective in reducing mean LDL cholesterol level.

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Problem 194

Estimate mean IQ of statistics students with 90% confidence and 4 IQ points precision. Given $\mu=100$ , $\sigma=13$ , find the required sample size.
The required sample size is $n = \left\lceil \frac{(1.645 \cdot 13)^2}{4^2} \right\rceil = 68$ . Would it be reasonable to sample this number of students? Yes. This number of IQ test scores is a fairly small number.

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Problem 195

Find the mean travel time for 6 students. Their travel times are $9, 15, 3, 16, 5, 11$ minutes. Round the mean to the nearest tenth.

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Problem 196

Find the coefficient of determination given the correlation coefficient $r = 0.566$ .

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Problem 197

Identify random variables from given options: $i)$ rainfall, $ii)$ student major, $iii)$ library book purchases. Select the correct answer.

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Problem 198

Fifty-four anesthetized wild bears were measured for weights and chest sizes. Is there sufficient evidence of a linear correlation between weights and chest sizes? Can chest size be used to predict weight? Use $\alpha=0.05$ .
Correlation Results: Correlation coeff, r: 0.965434 Critical r: ±0.2680855 P-value (two tailed): 0.000
Determine the null and alternative hypotheses: $H_{0}: \rho = 0$ $H_{1}: \rho \neq 0$

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Problem 199

Sample of 50 has mean $\bar{x}=25$ . Population std. dev. $\sigma=5$ . (a) Find standard error of mean $\sigma/\sqrt{n}$ . (b) At 95% conf., find margin of error $\pm z_{\alpha/2}\sigma/\sqrt{n}$ .

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Problem 200

Identify the sampling method used for a sample of every 49th student from 496 students: $A.$ Convenience, $B.$ Random, $C.$ Systematic, $D.$ Cluster, $E.$ Stratified.

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Statistics

Problem 101

Which score has the highest relative position given the mean Xˉ\bar{X}Xˉ and standard deviation sss?

Problem 102

Find the mean of the discrete distribution with X={4,6}X = \{4, 6\}X={4,6} and P(X)={0.51,0.49}P(X) = \{0.51, 0.49\}P(X)={0.51,0.49}.

Problem 103

Find the range (difference between largest and smallest values) of the data [101,521,125,325,107,125,917][101, 521, 125, 325, 107, 125, 917][101,521,125,325,107,125,917].

Problem 104

Problem 105

Determine if two independent samples from normal populations have equal means using a two-tailed test at α=0.05\alpha = 0.05α=0.05. The test statistic is t=−1.67t = -1.67t=−1.67, and the p-value is □\square□.

Problem 106

Problem 107

Problem 108

Find the p-value for a two-tailed test with test statistic z=−1.225z=-1.225z=−1.225 to determine if the proportion of men over 50 who regularly have their prostate examined is significantly different from 0.16.

Problem 109

Fill in the blank: A histogram aids in analyzing the shape of the distribution\text{shape of the distribution}shape of the distribution of the data.

Problem 110

A new film received a median rating of 7.237.237.23 stars. The first and third quartiles are 2.782.782.78 and 8.248.248.24 stars, respectively. What is the most likely statement?

Problem 111

Find the percentage of bolts with diameter > 0.320.320.32 inches, given the bolt diameters are normally distributed with mean 0.300.300.30 inches and standard deviation 0.010.010.01 inches. Round to 2 decimal places.

Problem 112

Find the most common birth weight among 8 babies with weights 4,5,5,3,5,4,5,44, 5, 5, 3, 5, 4, 5, 44,5,5,3,5,4,5,4 kg.

Problem 113

Find the range of time taken by students on a recent exam, given a bell-shaped distribution with μ=45.3\mu = 45.3μ=45.3 minutes and σ=5.6\sigma = 5.6σ=5.6 minutes, using the range rule of thumb.

Problem 114

Determine the set of data represented by the given stem-and-leaf plot: 7 3,4,5; 6 2,7; 5 1,3,47 \, 3, 4, 5; \, 6 \, 2, 7; \, 5 \, 1, 3, 473,4,5;62,7;51,3,4

Problem 115

Find the probability P(Z>−0.93)P(Z > -0.93)P(Z>−0.93) for the standard normal variable ZZZ. Round the answer to at least three decimal places.

Problem 116

Identify outliers among the 11 sandwich calorie values: 593,594,595,596,599,602,604,604,605,606,607593, 594, 595, 596, 599, 602, 604, 604, 605, 606, 607593,594,595,596,599,602,604,604,605,606,607.

Problem 117

Select the appropriate term to describe the information collected about individuals. The characteristics are called variables\mathbf{variables}variables.

Problem 118

Calculate the standard deviation of the given data: x={−8,−7,−6,−5,−4,−3}x = \{-8, -7, -6, -5, -4, -3\}x={−8,−7,−6,−5,−4,−3} and P(X=x)={0.1,0.1,0.2,0.1,0.3,0.2}P(X=x) = \{0.1, 0.1, 0.2, 0.1, 0.3, 0.2\}P(X=x)={0.1,0.1,0.2,0.1,0.3,0.2}. Round the answer to one decimal place.

Problem 119

Find the average of the numbers 62,61,46,61,5062, 61, 46, 61, 5062,61,46,61,50 and round the result to the nearest tenth.

Problem 120

Problem 121

Seat belt usage affects deaths. For every 1% increase in usage, deaths decrease by 280. Find the slope bbb and predict deaths if (i) 0%, (ii) 74%, (iii) 100% wear seat belts, given yyy-intercept is 28,910.a. The slope is b=−280b = -280b=−280.

Problem 122

Find the average length of the fish in the tank: 2,3,1,4,5,2,22, 3, 1, 4, 5, 2, 22,3,1,4,5,2,2. Round the mean to the nearest tenth.

Problem 123

Given a stem-and-leaf plot, find the mean, median, mode, and sample size of the distribution. 300.6,231.5,135.0,10300.6, 231.5, 135.0, 10300.6,231.5,135.0,10 or 271,217,272,5271, 217, 272, 5271,217,272,5 or 32,32,35,1032, 32, 35, 1032,32,35,10 or 18.2,20,20,518.2, 20, 20, 518.2,20,20,5.

Problem 124

Claim that the standard deviation of adult male pulse rates is less than 10 beats/min. For a sample of 138 males, the standard deviation is 8.58.58.5 beats/min. Find the test statistic.

Problem 125

Berechne Mittelwert, Median und Quartilsabstand für die Datenreihe: 3;8;12;5;7;8;9,5;11;14;6;8,53 ; 8 ; 12 ; 5 ; 7 ; 8 ; 9,5 ; 11 ; 14 ; 6 ; 8,53;8;12;5;7;8;9,5;11;14;6;8,5.

Problem 126

Evaluate the formula E=zp^(1−p^)nE=z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}E=znp^​(1−p^​)​​ for given values of zzz, p^\hat{p}p^​, and nnn. Round the result to three decimal places.

Problem 127

Find the percentage of people with IQ scores between 888888 and 116116116 in a normal distribution with μ=100\mu=100μ=100 and σ=15\sigma=15σ=15, rounded to the nearest tenth.

Problem 128

Find power function y=a×bxy=a \times b^xy=a×bx and linear function y=mx+cy=mx+cy=mx+c to model data set (x,y)(x, y)(x,y). Power function coefficients a=4.287a=4.287a=4.287, b=1.204b=1.204b=1.204. Determine which function better fits the data.

Problem 129

Find the best predicted IQ score y^\hat{y}y^​ for a wife given her husband's IQ of 979797, using a significance level of 0.050.050.05, where xˉ=101.08\bar{x}=101.08xˉ=101.08, yˉ=101.25\bar{y}=101.25yˉ​=101.25, r=0.825r=0.825r=0.825, and y^=10.2+0.9x\hat{y}=10.2+0.9xy^​=10.2+0.9x.

Problem 130

For a survey of 18-year-old males, find the weights representing the 99th, 43rd, and first quartile percentiles given a mean of 167.5167.5167.5 pounds and a standard deviation of 48.648.648.6 pounds.

Problem 131

Find the r-value with the strongest negative correlation: −0.9-0.9−0.9, −0.6-0.6−0.6, −0.7-0.7−0.7, or −0.8-0.8−0.8.

Problem 132

Problem 133

Find the percentile for the data value 125125125 in the given set: 119,131,123,117,125,127,117,115,122,119,123,133,115,119,121,116119, 131, 123, 117, 125, 127, 117, 115, 122, 119, 123, 133, 115, 119, 121, 116119,131,123,117,125,127,117,115,122,119,123,133,115,119,121,116.

Problem 134

Analyze the trend in women's finishers at the NYC Marathon from 1997 to 2001 using a scatter plot and describe any relationship.

Problem 135

In a survey of 254 students, 86%86\%86% enjoyed their classes. Find the margin of error, rounded to the nearest tenth of a percent.

Problem 136

Find the degrees of freedom for the given t-interval: xˉ=17.598\bar{x}=17.598xˉ=17.598, sx=16.01712719s_x=16.01712719sx​=16.01712719, n=50n=50n=50.

Problem 137

Estimate the proportion of first-time customers from a sample of 129 orders, given that 36% of orders come from first-time customers. Find the probability that the sample proportion is between 0.29 and 0.41.

Problem 138

Find a 99% confidence interval for the true mean lifetime of a brand of light bulbs with a sample of 80 bulbs having a mean lifetime of 497497497 hours and a standard deviation of 454545 hours. The lower and upper limits are 488.5488.5488.5 and 505.5505.5505.5 hours, respectively.

Problem 139

The median ticket price for musicals is 95andfornon−musicalplaysis95 and for non-musical plays is 95andfornon−musicalplaysis80. Calculate the difference in median ticket costs between musicals and non-musical plays.

Problem 140

Find the class with the highest average and least score variability from {A,B,C,D}\{A, B, C, D\}{A,B,C,D} where each class has a range of {56,55,48,57}\{56, 55, 48, 57\}{56,55,48,57} and mean scores {107,114,108,105}\{107, 114, 108, 105\}{107,114,108,105}.

Problem 141

Problem 142

Find the range of the values in the table, where X={−1,3,3,4}X = \{-1, 3, 3, 4\}X={−1,3,3,4} and Y={−2,0,−2,5}Y = \{-2, 0, -2, 5\}Y={−2,0,−2,5}.

Problem 143

Which score has the highest relative position given the mean $\bar{X}$ and standard deviation $s$ ?

Find the mean of the discrete distribution with $X = \{4, 6\}$ and $P(X) = \{0.51, 0.49\}$ .

Find the range (difference between largest and smallest values) of the data $[101, 521, 125, 325, 107, 125, 917]$ .

Determine if two independent samples from normal populations have equal means using a two-tailed test at $\alpha = 0.05$ . The test statistic is $t = -1.67$ , and the p-value is $\square$ .

Find the p-value for a two-tailed test with test statistic $z=-1.225$ to determine if the proportion of men over 50 who regularly have their prostate examined is significantly different from 0.16.

Fill in the blank: A histogram aids in analyzing the $\text{shape of the distribution}$ of the data.

A new film received a median rating of $7.23$ stars. The first and third quartiles are $2.78$ and $8.24$ stars, respectively. What is the most likely statement?

Find the percentage of bolts with diameter > $0.32$ inches, given the bolt diameters are normally distributed with mean $0.30$ inches and standard deviation $0.01$ inches. Round to 2 decimal places.

Find the most common birth weight among 8 babies with weights $4, 5, 5, 3, 5, 4, 5, 4$ kg.

Find the range of time taken by students on a recent exam, given a bell-shaped distribution with $\mu = 45.3$ minutes and $\sigma = 5.6$ minutes, using the range rule of thumb.

Determine the set of data represented by the given stem-and-leaf plot: $7 \, 3, 4, 5; \, 6 \, 2, 7; \, 5 \, 1, 3, 4$

Find the probability $P(Z > -0.93)$ for the standard normal variable $Z$ . Round the answer to at least three decimal places.

Identify outliers among the 11 sandwich calorie values: $593, 594, 595, 596, 599, 602, 604, 604, 605, 606, 607$ .

Select the appropriate term to describe the information collected about individuals. The characteristics are called $\mathbf{variables}$ .

Calculate the standard deviation of the given data: $x = \{-8, -7, -6, -5, -4, -3\}$ and $P(X=x) = \{0.1, 0.1, 0.2, 0.1, 0.3, 0.2\}$ . Round the answer to one decimal place.

Find the average of the numbers $62, 61, 46, 61, 50$ and round the result to the nearest tenth.

Seat belt usage affects deaths. For every 1% increase in usage, deaths decrease by 280. Find the slope $b$ and predict deaths if (i) 0%, (ii) 74%, (iii) 100% wear seat belts, given $y$ -intercept is 28,910.
a. The slope is $b = -280$ .

Find the average length of the fish in the tank: $2, 3, 1, 4, 5, 2, 2$ . Round the mean to the nearest tenth.

Given a stem-and-leaf plot, find the mean, median, mode, and sample size of the distribution. $300.6, 231.5, 135.0, 10$ or $271, 217, 272, 5$ or $32, 32, 35, 10$ or $18.2, 20, 20, 5$ .

Claim that the standard deviation of adult male pulse rates is less than 10 beats/min. For a sample of 138 males, the standard deviation is $8.5$ beats/min. Find the test statistic.

Berechne Mittelwert, Median und Quartilsabstand für die Datenreihe: $3 ; 8 ; 12 ; 5 ; 7 ; 8 ; 9,5 ; 11 ; 14 ; 6 ; 8,5$ .

Evaluate the formula $E=z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$ for given values of $z$ , $\hat{p}$ , and $n$ . Round the result to three decimal places.

Find the percentage of people with IQ scores between $88$ and $116$ in a normal distribution with $\mu=100$ and $\sigma=15$ , rounded to the nearest tenth.

Find power function $y=a \times b^x$ and linear function $y=mx+c$ to model data set $(x, y)$ . Power function coefficients $a=4.287$ , $b=1.204$ . Determine which function better fits the data.

Find the best predicted IQ score $\hat{y}$ for a wife given her husband's IQ of $97$ , using a significance level of $0.05$ , where $\bar{x}=101.08$ , $\bar{y}=101.25$ , $r=0.825$ , and $\hat{y}=10.2+0.9x$ .

For a survey of 18-year-old males, find the weights representing the 99th, 43rd, and first quartile percentiles given a mean of $167.5$ pounds and a standard deviation of $48.6$ pounds.

Find the r-value with the strongest negative correlation: $-0.9$ , $-0.6$ , $-0.7$ , or $-0.8$ .

Find the percentile for the data value $125$ in the given set: $119, 131, 123, 117, 125, 127, 117, 115, 122, 119, 123, 133, 115, 119, 121, 116$ .

In a survey of 254 students, $86\%$ enjoyed their classes. Find the margin of error, rounded to the nearest tenth of a percent.

Find the degrees of freedom for the given t-interval: $\bar{x}=17.598$ , $s_x=16.01712719$ , $n=50$ .

Find a 99% confidence interval for the true mean lifetime of a brand of light bulbs with a sample of 80 bulbs having a mean lifetime of $497$ hours and a standard deviation of $45$ hours. The lower and upper limits are $488.5$ and $505.5$ hours, respectively.

The median ticket price for musicals is $95 and for non-musical plays is$ 80. Calculate the difference in median ticket costs between musicals and non-musical plays.

Find the class with the highest average and least score variability from $\{A, B, C, D\}$ where each class has a range of $\{56, 55, 48, 57\}$ and mean scores $\{107, 114, 108, 105\}$ .

Find the range of the values in the table, where $X = \{-1, 3, 3, 4\}$ and $Y = \{-2, 0, -2, 5\}$ .

Determine the probability a person aged 46+ prefers cash payment from the given data.
$P(\text{Cash} | \text{Age } 46+) = \frac{35}{35 + 25}$

Create a stem-and-leaf display with $3 \le$ stem values $\le 10$ , $1 \le$ leaf values $\le 100$ , and at least $20$ leaf values between $5$ and $20$ .

Determine if a statistics student's calculated mean $\bar{x}=-10$ is possible.

Find the average rate of change in public library visits from 1997 ( $1.4$ billion) to 2001 ( $1.5$ billion). The average rate of change was $0.025$ billion per year.

Find the modes of the data set $5, 6, 4, 4, 4, 3, 7, 3, 3, 7, 7$ . If there is more than one mode, write them separated by commas. If there is no mode, click on "No mode."

Complete a table for 5 graph values. Given mean of 5, calculate distance of each score $X=1, X=6, x=7, x=7, x=8$ from the mean.

Determine the meaning of the constant 378 in the equation $n=-38 g+378$ that models the number of students $n$ in grade $g$ at an elementary school.

Approximately what percentage of 1-mile Pennsylvania freeway segments have between 26 and 61 potholes, given a mean of $47$ and standard deviation of $7$ ?

Airline operations manager wants to survey air passengers to estimate percentage preferring aisle seats. Find sample sizes to be 99% confident within 1.5% of true percentage, given (a) no prior information and (b) 38% prefer aisle seats.
(a) $n = 7372$ (b) $n = 600$

Claim: More than $4.8\%$ of homes have only a landline phone, no wireless. Find symbolic expression for claim.

Asthma drug trial: 28 of 275 subjects had headaches. Test if headache rate is less than 12% at 1% significance level.
$z=-0.93$ , $p$ -value $= 0.18$ . The test is right-tailed.

Estimate the true proportion of adults who would like to travel to outer space with $93\%$ confidence. Use a graphing calculator and round the answer to at least three decimal places.

Estimate the mean height of all female students at a college using a random sample of 36 students. The sample mean is 65.3 inches and the standard deviation is 5.2 inches. Find the $90\%$ confidence interval for the true mean, assuming a normal distribution.

Estimate the proportion (p) of the voting population that prefers Candidate A, given that 80 out of 100 sampled people preferred A. Use a $99 \%$ confidence level and give the answer as a decimal to three places.

Find the percentage of $400 \mathrm{~W}$ light bulbs with lifetimes less than 720 hours, given a normal distribution with $\mu = 680$ hours and $\sigma = 125$ hours.

Find the probability that a randomly selected 8th grade student in the School of Rock plays the keyboard, expressed as a simplified fraction.
\text{Probability} = \frac{\text{# of 8th grade keyboard players}}{\text{Total # of 8th grade students}}

Car accident outcomes by seat belt usage: Probability of surviving accident without seat belt is $\frac{165,019}{166,888}$ .

Find two-sided critical values for a normal distribution at $z_{0.05}$ , $z_{0.025}$ , $z_{0.01}$ , and $z_{0.005}$ given $z_{0.10} = 1.28$ .

A company claims the mean caffeine content of its 12-oz cola is 40 mg. You test a sample of 30 bottles and find the mean is 37.8 mg. At $\alpha=0.09$ , can you reject the company's claim? Determine the appropriate hypothesis test and critical value(s).

Construct a scatterplot to show the relationship between protein and carbohydrate content for 12 bean varieties, using carbohydrate content ( $x$ -axis) and protein content ( $y$ -axis).

Calculate the probabilities of a home pregnancy test given the results: $P($ positive $\mid$ pregnant $)$ , $P($ pregnant $\mid$ positive $)$ , $P($ negative $\mid$ pregnant $)$ , and $P($ not pregnant $\mid$ negative $)$ . Round the answers to the nearest thousandth.

Find $z$ such that 0.6826 of the area lies between $-z$ and $z$ . Round $z$ to two decimal places.