The shape of the distribution of the time required to get an oil change at a 10-minute oil-change facility is unknown. However, records indicate that the mean time for an oil change is 11.4 minutes, and the standard deviation for oil-change time is 3.2 minutes.

(a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required?

(b) What is the probability that a random sample of n = 40 oil changes results in a sample mean time of less than 10 minutes?

(c) 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 40 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.