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

To compute probabilities regarding the sample mean using the normal​ model, what size sample would be​ required? Choose the required sample size below.

A. Any sample size could be used.

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

C. The sample size needs to be greater than 30.

D. The sample size needs to be less than 30. ​

(b) What is the probability that a random sample of n=35 oil changes results in a sample mean time less than 15 ​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

35 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.

Answer 1

The solution to this problem is given by