7.1 & 7.2 QUIZ

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 0.7357

-0.63

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 0.8888

-1.22

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Round to four decimal places. -1.82/1.82

0

Find the critical value zα/2 that corresponds to the confidence level 84​%.

1.41

Find the critical value zα/2 that corresponds to the given confidence level. 89​%

1.60

Find the critical value zα/2 that corresponds to the confidence level 90​%.

1.65

Find the critical value zα/2 that to the confidence level 94​%.

1.88

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 90​% of all males.​ (Accommodating 100% of males would require very wide seats that would be much too​ expensive.) Men have hip breadths that are normally distributed with a mean of 14.7 in. and a standard deviation of 0.8 in. Find P90. That​ is, find the hip breadth for men that separates the smallest 90​% from the largest 10​%.

15.7 in

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 90​% of all males.​ (Accommodating 100% of males would require very wide seats that would be much too​ expensive.) Men have hip breadths that are normally distributed with a mean of 14.8 in. and a standard deviation of 0.9 in. Find P90. That​ is, find the hip breadth for men that separates the smallest 90​% from the largest 10​%.

16.0

Find the critical value zα/2 that corresponds to the given confidence level. 99​%

2.58

Listed below are student evaluation ratings of​ courses, where a rating of 5 is for​ "excellent." The ratings were obtained at one university in a state. Construct a confidence interval using a 99​% confidence level. What does the confidence interval tell about the population of all college students in the​ state? 4.0​, 2.8​, 4.2​, 4.7​, 3.0​, 4.4​, 3.3​, 4.3​, 4.5​, 4.2​, 4.5​, 3.6​, 3.5​, 3.8​, 4.0

3.48 < 4.36 The results tell nothing about the population of all college students in the​ state, since the sample is from only one university.

Listed below are the amounts of net worth​ (in millions of​ dollars) of the ten wealthiest celebrities in a country. Construct a 99​% confidence interval. What does the result tell us about the population of all​ celebrities? Do the data appear to be from a normally distributed population as​ required?

A: $135.3 MILLION < $209.3 MILLION B: What does the result tell us about the population of all​ celebrities? Select the correct choice below​ and, if​ necessary, fill in the answer​ box(es) to complete your choice. B: Because the ten wealthiest celebrities are not a representative​ sample, this​ doesn't provide any information about the population of all celebrities. C: No, because the points lie reasonable close to a straight​ line, but there is a systematic pattern that is not a straight line pattern.

Listed below are the amounts of net worth​ (in millions of​ dollars) of the ten wealthiest celebrities in a country. Construct a 99​% confidence interval. What does the result tell us about the population of all​ celebrities? Do the data appear to be from a normally distributed population as​ required? 250 193 182 172 169 155 145 145 145 145

A: $136.2 < $ 204.0 B: Because the ten wealthiest celebrities are not a representative​ sample, this​ doesn't provide any information about the population of all celebrities. C: No, because the points lie reasonable close to a straight​ line, but there is a systematic pattern that is not a straight line pattern.

Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n=1036 and x=548 who said​ "yes." Use a 90% confidence level.

A: 0.529 B: 0.025 C: 0.504 < p < 0.554 D: One has 90​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n=1066 and x=584 who said​ "yes." Use a 90% confidence level.

A: 0.548 B: 0.025 C: 0.0523 < p < 0.573 D: One has 90​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n=930 and x=592 who said​ "yes." Use a 99% confidence level.

A: 0.637 B: 0.041 C: 0.0596 < p < 0.677 D: One has 99​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

Listed below are student evaluation ratings of​ courses, where a rating of 5 is for​ "excellent." The ratings were obtained at one university in a term-1state. Construct a confidence interval using a 95​% confidence level. What does the confidence interval tell about the population of all college students in the​ state? 3.6​, 3.1​, 4.1​, 4.9​, 2.9​, 4.0​, 3.3​, 4.8​, 4.3​, 4.5​, 4.2​, 4.1​, 3.1​, 3.7​, 3.8

A: 3.55 < 4.23 B: The results tell nothing about the population of all college students in the​ state, since the sample is from only one university.

Listed below are student evaluation ratings of​ courses, where a rating of 5 is for​ "excellent." The ratings were obtained at one university in a term-1state. Construct a confidence interval using a 90​% confidence level. What does the confidence interval tell about the population of all college students in the​ state? 4.0​, 3.2​, 4.1​, 4.7​, 2.9​, 4.1​, 3.4​, 4.7​, 4.7​, 4.1​, 4.4​, 3.7​, 3.0​, 4.1​, 3.9

A: 3.66 < 4.20 B: The results tell nothing about the population of all college students in the​ state, since the sample is from only one university.

The overhead reach distances of adult females are normally distributed with a mean of 205 cm and a standard deviation of 8.6 cm. a. Find the probability that an individual distance is greater than 217.50 cm b. Find the probability that the mean for 20 randomly selected distances is greater than 203.70 cm c. Why can the normal distribution be used in part (b) even though the sample size does not exceed 30?

A: The probability is: 0.0730 B: 0.7505 C: The normal distribution can be used because the original population has a normal distribution.

The overhead reach distances of adult females are normally distributed with a mean of 202.5 cm and a standard deviation of 8.9 cm. a. Find the probability that an individual distance is greater than 211.80 cm b. Find the probability that the mean for 25 randomly selected distances is greater than 201.20 cm c. Why can the normal distribution be used in part (b) even though the sample size does not exceed 30?

A: The probability is: 0.1492 B: 0.7673 C: The normal distribution can be used because the original population has a normal distribution.

An IQ test is designed so that the mean is 100 and the standard deviation is 18 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99​% confidence that the sample mean is within 4 IQ points of the true mean. Assume that σ=18 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

A: The required sample size is= 135 or 139 B: Yes. This number of IQ test scores is a fairly small number.

An IQ test is designed so that the mean is 100 and the standard deviation is 20 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95​% confidence that the sample mean is within 4 IQ points of the true mean. Assume that σ=20 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

A: The required sample size is= 97 or 99 B: Yes. This number of IQ test scores is a fairly small number

An IQ test is designed so that the mean is 100 and the standard deviation is 23 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99​% confidence that the sample mean is within 6 IQ points of the true mean. Assume that σ=23 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

A: The required sample size is= 98 or 102 B: Yes. This number of IQ test scores is a fairly small number.

Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A drug is used to help prevent blood clots in certain patients. In clinical​ trials, among 4936 patients treated with the drug, 129 developed the adverse reaction of nausea. Construct a 99% confidence interval for the proportion of adverse reactions.

A= 0.026 B= 0.006 C= 0.020< p < 0.032 D= One has 95​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A drug is used to help prevent blood clots in certain patients. In clinical​ trials, among 4930 patients treated with the drug, 164 developed the adverse reaction of nausea. Construct a 95% confidence interval for the proportion of adverse reactions.

A= 0.033 B= 0.005 C= 0.028 < p < 0.038 D= One has 95​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

Which of the following is NOT a property of the sampling distribution of the sample​ mean?

The distribution of the sample mean tends to be skewed to the right or left.

Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. The results in the screen display are based on a​ 95% confidence level. Write a statement that correctly interprets the confidence interval. TInterval ​(13.046,22.15) x=17.598 Sx=16.01712719 n=50

We have​ 95% confidence that the limits of 13.05 Mbps and 22.15 Mbps contain the true value of the mean of the population of all data speeds at the airports.