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 is 11.8 minutes​, and the...

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

Choose the required sample size below.

​(b) What is the probability that a random sample of

oil changes results in a sample mean time less than

​minutes?

The probability is approximately

​(Round to four decimal places as​ needed.)

​(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

oil changes between 10 A.M. and 12 P.M. Treating this as a random​ sample, at 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.

There would be a​ 10% chance of being at or below

minutes.

​(Round to one decimal place as​ needed.)