Math Problem Solver

Use the standard normal distribution or the​ t-distribution to construct a 95​% confidence interval for the population mean. Justify your decision. If neither distribution can be​ used, explain why. Interpret the results.

In a recent​ season, the population standard deviation of the yards per carry for all running backs was 1.28. The yards per carry of 25 randomly selected running backs are shown below. Assume the yards per carry are normally distributed.

1.3

2.9

6.8

4.6

5.5

7.2

5.5

5.3

4.1

1.9

2.4

7.2

3.2

3.3

4.6

4.7

5.4

5.6

3.3

5.5

3.3

3.8

5.3

7.1

3.6

Question content area bottom

Part 1

Which distribution should be used to construct the confidence​ interval?

A.

Use a​ t-distribution because nless than30 and sigma is known.

B.

Use a normal distribution because sigma is known and the data are normally distributed.

Your answer is correct.C.

Use a​ t-distribution because nless than30 and sigma is unknown.

D.

Use a normal distribution because n less than 30​, the data are normally distributed and sigma is unknown.

E.

Cannot use the standard normal distribution or the​ t-distribution because sigma is​ unknown, n less than 30​, and the data are not normally distributed.

Part 2

Select the correct choice below​ and, if​ necessary, fill in any answer boxes to complete your choice.

A.

The 95​% confidence interval is ​(

enter your response here​,

enter your response here​).

​(Round to two decimal places as​ needed.)

B.

Neither distribution can be used to construct the confidence interval.