7.27 Average time to fill job positions For all job positions in a company, assume that, a few years ago, the average time to fill a job position was 37 days with a standard deviation of 12 days. For the purpose of comparison, the manager of the hiring department selected a random sample of 100 of today’s job positions. He observed a sample mean of 39 days and a standard deviation of 13 days.

a. Describe the center and variability of the population distribution. What shape does it probably have?

Explain.

b. Describe the center and variability of the data distribution.

What shape does it probably have? Explain.

c. Describe the center and variability of the sampling distribution of the sample mean for n = 100. What shape does it have? Explain.

d. Explain why it would not be unusual it would be highly unusual to observe a sample mean of more than 50 days for a random sample size of 100 job positions.