Question: (15) The owner of a large equipment rental company wants to make a rather quick estimate of the average number of days a piece of ditch digging equipment is rented out per person per time. The company has records of all rentals, but the amount of time required to conduct an audit of all accounts would be prohibitive. The owner decides to take a random sample of rental invoices. Fourteen different rentals of ditchdiggers are selected randomly form the files, yielding the following data.

3 1 3 2 5 1 2 1 4 2 1 3 1 1

Construct a 99% confidence interval to estimate the average number of days that a ditch digger is rented. Assume that the number of days per rental is normally distributed in the population.