The owner of a heavy machinery rental company wants to make a rather quick estimate of the average number of days that excavators are rented out to a client. The company has records of all excavator rentals previously made to its clients, but the amount of time required to conduct an audit of all these records would be prohibitive. From all of these company records, the owner decides to randomly select a sample of 14 rental invoices for excavators and records the number of days the excavator was rented out to a client the following data (in days) are collected.

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

Using these data, construct a 99% confidence interval to estimate the average number of days and excavator is rented to a client, and assume the number of days per rental is normally distributed in the population.