The shape of the distribution of the time required to get an oil change at a 20-minute oil-change Jiffy Lube is unknown.However, records indicate that the mean time is 21.2minutes, and the standard deviation is 4.7minutes. Complete parts (a) through (c).

(a) To compute probabilities regarding the sample mean using the normalmodel, what size sample would berequired?

A.

Any sample size could be used.

B.

The sample size needs to be less than or equal to 30.

C.

The sample size needs to be greater than or equal to 30.

D.

The normal model cannot be used if the shape of the distribution is unknown.

(b) What is the probability that a random sample of n=45 oil changes results in a sample mean time less than 20 minutes?

The probability is approximately

.

(Round to four decimal places asneeded.)

(c) Suppose the manager agrees to pay each employee a$20 bonus if they meet a certain goal. On a typicalSaturday, theoil-change facility will perform 45 oil changes between 10 A.M. and 8 P.M. Treating this as a randomsample, there would be a10% chance of the meanoil-change time being at or below whatvalue? This will be the goal established by the manager.

There is a10% chance of being at or below a meanoil-change time of

nothing

minutes.

(Round to one decimal place asneeded.)