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# Suppose the average commute time of your employees is unknown. The standard deviation of their commute time is estimated as 32.5 minutes.

1.Suppose the average commute time of your employees is unknown. The standard deviation of their commute time is estimated as 32.5 minutes.

**How many employees must be included in a sample to actualize a 95 percent confidence interval for the average commute time with a confidence interval width of no more than 15 minutes?**

Note that the correct answer will be evaluated based on the z-values in the summary table in the Teaching Materials section.

Remember to round your answer **up** to an integer.

Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.

2.Suppose you are working for a regional residential natural gas utility. For a sample of 90 customer visits, the staff time per reported gas leak has a mean of 211 minutes and standard deviation 31 minutes. The VP of network maintenance hypothesizes that the average staff time devoted to reported gas leaks is 219 minutes.

**At a 10 percent level of significance, what is the lower bound of the interval for determining whether to accept or reject the VP's hypothesis?**

Note that the correct answer will be evaluated based on the z-values in the summary table in the Teaching Materials section.

Please round your answer to the nearest tenth.

Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.