The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.2 minutes, and the standard deviation is 3.4 minutes.

(a) What is the probability that a random sample of n = 45 oil changes results in a sample mean time less than 10 minutes?
(b) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 45 oil changes between 10 A. M. and 12 P. M. Treating this as a random sample, what mean oil-change time would there be a 10% chance of being at or below? This will be the goal established by the manager.