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 40 oil changes results in a sample mean time less than 15 minutes?

(b) suppose the manager agrees to pay each employee a $50 bonus if they meet a certain gol. on a typical sunday, 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 1096 chance of being at or below? this will be the goal established by the manager. there is a 1096 chance of being at or below a mean oil change time of ? minutes.