# 6.1 Confidence Intervals with Standard Deviation Known

In a random sample of 60 computers, the mean repair cost was $150. Assume the population standard deviation is $36. Construct a 90% confidence interval for the population mean.

($142, $158)

A random sample of 40 students has a mean annual earnings of $3120. Assume the population standard deviation is $677. Construct the confidence interval for the population mean, μ if c = 0.95.

($2910, $3330)

In a recent study of 42 eighth graders, the mean number of hours per week that they watched television was 19.6. Assume the population standard deviation is 5.8 hours. Find the 98% confidence interval for the population mean.

(17.5, 21.7)

A group of 40 bowlers showed that their average score was 192. Assume the population standard deviation is 8. Find the 95% confidence interval of the mean score of all bowlers.

(189.5, 194.5)

A random sample of 150 students has a grade point average with a mean of 2.86. Assume the population standard deviation is 0.78. Construct the confidence interval for the population mean, μ, if c = 0.98.

(2.71, 3.01)

A group of 49 randomly selected students has a mean age of 22.4 years. Assume the population standard deviation is 3.8. Construct a 98% confidence interval for the population mean.

(21.1, 23.7)

In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches. From previous studies, it is assumed that the standard deviation σ is 2.4 and that the population of height measurements is normally distributed. Construct the 95% confidence interval for the population mean.

(61.9, 64.9)

A random sample of 56 fluorescent light bulbs has a mean life of 645 hours. Assume the population standard deviation is 31 hours. Construct a 95% confidence interval for the population mean.

(636.9, 653.1)

A random sample of 40 students has a test score with = 81.5. Assume the population standard deviation is 10.2. Construct the confidence interval for the population mean, μ if c = 0.90.

(78.8, 84.2)

Find the margin of error for the given values of c, σ, and n.c = 0.95, σ = 677, n = 40

$210

Determine the sampling error if the grade point averages for 10 randomly selected students from a class of 125 students has a mean of = 2.3. Assume the grade point average of the 125 students has a mean of

-0.4

Find the margin of error for the given values of c, σ, and n.c = 0.98, σ = 0.78, n = 150

0.15

Find the margin of error for the given values of c, σ, and n.c = 0.90, σ = 10.2, n = 75

1.94

In order to efficiently bid on a contract, a contractor wants to be 95% confident that his error is less than two hours in estimating the average time it takes to install tile flooring. Previous contracts indicate that the standard deviation is 4.5 hours. How large a sample must be selected?

20

In order to fairly set flat rates for auto mechanics, a shop foreman needs to estimate the average time it takes to replace a fuel pump in a car. How large a sample must he select if he wants to be 99% confident that the true average time is within 15 minutes of the sample average? Assume the standard deviation of all times is 30 minutes.

27

In order to set rates, an insurance company is trying to estimate the number of sick days that full time workers at an auto repair shop take per year. A previous study indicated that the standard deviation was 2.8 days. How large a sample must be selected if the company wants to be 95% confident that the true mean differs from the sample mean by no more than 1 day?

31

A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 99% confident that the true mean is within 4 ounces of the sample mean? The standard deviation of the birth weights is known to be 9 ounces.

34

The standard IQ test has a mean of 97 and a standard deviation of 17. We want to be 95% certain that we are within 5 IQ points of the true mean. Determine the required sample size.

45

Find the critical value zc that corresponds to a 98% confidence level.

±2.33