A simple random sample of 50 calls is monitored at an in-bound call center and the average length of the calls is 6.5 minutes. The population...

1.     A simple random sample of 50 calls is monitored at an in-bound call center and the average length of the calls is 6.5 minutes. The population standard deviation σ is unknown. Instead the sample standard deviation s is also calculated from the sample and is found to be 4.5 minutes.

a.     Construct a 99% confidence interval (using the t-distribution) for the average length of inbound calls.

b.     What is the margin of error at the 95% confidence level?

c.      Do we need to make any assumption on the distribution of the length of in-bound calls at this call center? Why or why not?