# STAT 2110 Test Chapters 6 and 7

STAT 2110 Test Chapters 6 and 7

Show any work that you can, so that I may give you partial credit if you don't get the final answer correct.

If you need more space, feel free to attach additional sheets. Just be sure to identify which problem you are working on

on the additional sheets.

1) Find the area of the shaded region. The graph depicts IQ scores of adults, and those scores are normally

distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).

2) Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of

15 (as on the Wechsler test). Find the IQ score separating the top 14% from the others.

3) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a

standard deviation of 50. Find P60, the score which separates the lower 60% from the top 40%.

1

4) The weights of certain machine components are normally distributed with a mean of 8.01 g and a standard

deviation of 0.06 g. Find the two weights that separate the top 3% and the bottom 3%. These weights could serve

as limits used to identify which components should be rejected. Round to the nearest hundredth of a gram.

Assume that X has a normal distribution, and find the indicated probability.

5) The mean is μ= 15.2 and the standard deviation is = 0.9.

Find the probability that X is greater than 16.1.

Find the indicated probability.

6) The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation

of $150. What percentage of trainees earn less than $900 a month?

7) In one region, the September energy consumption levels for single-family homes are found to be normally

distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a randomly selected home, find

the probability that the September energy consumption level is between 1100 kWh and 1225 kWh.

2

Solve the problem.

8) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 109

inches, and a standard deviation of 10 inches. What is the probability that the mean annual precipitation during

25 randomly picked years will be less than 111.8 inches?

9) Assume that women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of

2.5 inches. If 90 women are randomly selected, find the probability that they have a mean height between 62.9

inches and 64.0 inches.

10) A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier

shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected,

find the probability that their mean rebuild time exceeds 8.7 hours.

3

11) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected,

find the probability that the mean of their test scores is less than 76.

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

12) n = 130, x = 69; 90% confidence

Use the given data to find the minimum sample size required to estimate the population proportion.

13) ^ Margin of error: 0.07; confidence level: 95%; from a prior study, p is estimated by the decimal equivalent of 92%.

4

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

14) A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct

the 95% confidence interval for the true proportion of all voters in the state who favor approval.

15) Of 260 employees selected randomly from one company, 18.46% of them commute by carpooling. Construct a

90% confidence interval for the true percentage of all employees of the company who carpool.

Solve the problem.

16) In a certain population, body weights are normally distributed with a mean of 152 pounds and a standard

deviation of 26 pounds. How many people must be surveyed if we want to estimate the percentage who weigh

more than 180 pounds? Assume that we want 96% confidence that the error is no more than 4 percentage points.

5

Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume

that the population has a normal distribution.

17) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams

with s = 17.6 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such

eggs.

18) The football coach randomly selected ten players and timed how long each player took to perform a certain

drill. The times (in minutes) were:

7.0 10.8 9.5 8.0 11.5

7.5 6.4 11.3 10.2 12.6

Determine a 95% confidence interval for the mean time for all players.

Find the mean and standard deviation of this sample by using the Descriptive Statistics on your TI 84.

Directions can be found in the TESTS folder on Blackboard.

6

Use the given information to find the minimum sample size required to estimate an unknown population mean μ.

19) How many women must be randomly selected to estimate the mean weight of women in one age group. We

want 90% confidence that the sample mean is within 3.4 lb of the population mean, and the population standard

deviation is known to be 25 lb.

Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your

answer to the same number of decimal places as the sample mean.

20) A random sample of 187 full-grown lobsters had a mean weight of 19 ounces and a standard deviation of 3.3

ounces. Construct a 98% confidence interval for the population mean μ.

7

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation .

Assume that the population has a normal distribution. Round the confidence interval limits to the same number of

decimal places as the sample standard deviation.

21) The mean replacement time for a random sample of 20 washing machines is 10.9 years and the standard

deviation is 2.7 years. Construct a 99% confidence interval for the standard deviation, , of the replacement

times of all washing machines of this type.

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation .

Assume that the population has a normal distribution. Round the confidence interval limits to one more decimal place

than is used for the original set of data. Find the mean and standard deviation of this data by using the Descriptive

Statistics on your TI 84. Directions can be found in the TESTS folder on Blackboard.

22) The football coach randomly selected ten players and timed how long each player took to perform a certain

drill. The times (in minutes) were:

9 7 15 6 15

12 8 6 14 5

Find a 95% confidence interval for the population standard deviation .

8

Show any work that you can, so that I may give you partial credit if you don't get the final answer correct.

If you need more space, feel free to attach additional sheets. Just be sure to identify which problem you are working on

on the additional sheets.

1) Find the area of the shaded region. The graph depicts IQ scores of adults, and those scores are normally

distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).

2) Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of

15 (as on the Wechsler test). Find the IQ score separating the top 14% from the others.

3) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a

standard deviation of 50. Find P60, the score which separates the lower 60% from the top 40%.

1

4) The weights of certain machine components are normally distributed with a mean of 8.01 g and a standard

deviation of 0.06 g. Find the two weights that separate the top 3% and the bottom 3%. These weights could serve

as limits used to identify which components should be rejected. Round to the nearest hundredth of a gram.

Assume that X has a normal distribution, and find the indicated probability.

5) The mean is μ= 15.2 and the standard deviation is = 0.9.

Find the probability that X is greater than 16.1.

Find the indicated probability.

6) The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation

of $150. What percentage of trainees earn less than $900 a month?

7) In one region, the September energy consumption levels for single-family homes are found to be normally

distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a randomly selected home, find

the probability that the September energy consumption level is between 1100 kWh and 1225 kWh.

2

Solve the problem.

8) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 109

inches, and a standard deviation of 10 inches. What is the probability that the mean annual precipitation during

25 randomly picked years will be less than 111.8 inches?

9) Assume that women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of

2.5 inches. If 90 women are randomly selected, find the probability that they have a mean height between 62.9

inches and 64.0 inches.

10) A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier

shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected,

find the probability that their mean rebuild time exceeds 8.7 hours.

3

11) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected,

find the probability that the mean of their test scores is less than 76.

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

12) n = 130, x = 69; 90% confidence

Use the given data to find the minimum sample size required to estimate the population proportion.

13) ^ Margin of error: 0.07; confidence level: 95%; from a prior study, p is estimated by the decimal equivalent of 92%.

4

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

14) A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct

the 95% confidence interval for the true proportion of all voters in the state who favor approval.

15) Of 260 employees selected randomly from one company, 18.46% of them commute by carpooling. Construct a

90% confidence interval for the true percentage of all employees of the company who carpool.

Solve the problem.

16) In a certain population, body weights are normally distributed with a mean of 152 pounds and a standard

deviation of 26 pounds. How many people must be surveyed if we want to estimate the percentage who weigh

more than 180 pounds? Assume that we want 96% confidence that the error is no more than 4 percentage points.

5

Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume

that the population has a normal distribution.

17) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams

with s = 17.6 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such

eggs.

18) The football coach randomly selected ten players and timed how long each player took to perform a certain

drill. The times (in minutes) were:

7.0 10.8 9.5 8.0 11.5

7.5 6.4 11.3 10.2 12.6

Determine a 95% confidence interval for the mean time for all players.

Find the mean and standard deviation of this sample by using the Descriptive Statistics on your TI 84.

Directions can be found in the TESTS folder on Blackboard.

6

Use the given information to find the minimum sample size required to estimate an unknown population mean μ.

19) How many women must be randomly selected to estimate the mean weight of women in one age group. We

want 90% confidence that the sample mean is within 3.4 lb of the population mean, and the population standard

deviation is known to be 25 lb.

Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your

answer to the same number of decimal places as the sample mean.

20) A random sample of 187 full-grown lobsters had a mean weight of 19 ounces and a standard deviation of 3.3

ounces. Construct a 98% confidence interval for the population mean μ.

7

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation .

Assume that the population has a normal distribution. Round the confidence interval limits to the same number of

decimal places as the sample standard deviation.

21) The mean replacement time for a random sample of 20 washing machines is 10.9 years and the standard

deviation is 2.7 years. Construct a 99% confidence interval for the standard deviation, , of the replacement

times of all washing machines of this type.

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation .

Assume that the population has a normal distribution. Round the confidence interval limits to one more decimal place

than is used for the original set of data. Find the mean and standard deviation of this data by using the Descriptive

Statistics on your TI 84. Directions can be found in the TESTS folder on Blackboard.

22) The football coach randomly selected ten players and timed how long each player took to perform a certain

drill. The times (in minutes) were:

9 7 15 6 15

12 8 6 14 5

Find a 95% confidence interval for the population standard deviation .

8

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