Consider a dentist's office where the waiting room times U are uniformly distributed between 0 and 12 minutes(I.E. U- Uniform(0,12)).

a. standard deviation for the waiting times at this dentist's office is 3.464. Suppose that you randomly observed 17 patients' waiting times. You then compute the sample mean of these observations. Approximately what distribution does the sampling distribution U of these observations follow (hint the new sampling distribution is specified by a mean and standard deviation)? State the type of distribution type as well as the mean and variance.

b. What is the probability that the sample mean U of the 17 recorded waiting times is less than 5 minutes (round to three decimal places)?

c. What is the 99th percentile of the sample mean waiting time when there are 17 observed waiting times and the distribution is as listed above (round your answer to three decimal places)?