Unit 4 Lesson 5

Assignment

1. A company that produces white bread is concerned about the distribution of the amount of sodium in its

bread. The company takes a simple random sample of 100 slices of bread and computes the sample mean to be

103 milligrams of sodium per slice. Construct a 99\% confidence interval for the unknown mean sodium level

assuming that the population standard deviation is 10 milligrams. Write a sentence explaining what this

confidence interval means.

2. You work for a consumer advocate agency and want to find the mean repair cost of a washing machine. In

the past, the standard deviation of the cost of repairs for washing machines has been $17.50. As part of your

study, you randomly select 40 repair costs and find the mean to be $100.00. Calculate a 90\% confidence

interval for the population mean.

3. The actual time it takes to cook a ten pound turkey is a normally distributed. Suppose that a random sample

of 19 ten pound turkeys is taken. Given that an average of 2.9 hours and a standard deviation of .24 hours was

found for a sample of 19 turkeys, calculate a 90\% confidence interval for the average cooking time of a ten

pound turkey.

4. An engineer at a bolt factory knows that the widths of the bolts produced on a given day are normally

distributed with a standard deviation of o = 0.2 mm. She chooses an SRS of 15 bolts from the days production

and measures their widths. The measurements (in millimeters) are as follows: 9.87 9.83 9.71 10.09 10.04 9.67 9.62 9.89 9.89 9.99 10.31 10.31 10.05 10.06 9.73 9.96. Find the 95\% confidence interval for the population mean of the distribution.

5. Suppose we know that scores on a standardized reading exam are normally distributed with a standard

deviation of o = 130. We choose an SRS of 300 exams and find that the sample mean of the scores is x =

509.23.

Find the 99\% confidence interval for the population mean of the distribution. 6. A political organization claims that the population mean score on a standardized math exam is above 325.

We know that the scores are normally distributed with a standard deviation of o = 55. Suppose we 300 students

took the exam and we found that the sample mean of the scores is x = 315. Find the 95\% confidence interval for

the population mean of the distribution.

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