Question

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 16.3 minutes​, and the standard deviation is 4.3 minutes. Complete parts ​(a) through ​(c).

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

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

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

C. Any sample size could be used.

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

​

(b) What is the probability that a random sample of nequals 35 oil changes results in a sample mean time less than 15 ​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 35 oil changes between 10 A.M. and 12 P.M. Treating this as a random​ sample, there would be a​ 10% chance of the mean​ oil-change time being at or below what​ value? This will be the goal established by the manager.

There is a​ 10% chance of being at or below a mean​ oil-change time of

nothing minutes.

Answer 1

thank you.