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 16.2 minutes, and the standard deviation is 3.4 minutes.

Requried:
a. What is the probabilty 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 goal. On a typical​ Saturday, the​ oil-change facility will perform 40 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.

Answer 1

Answer:

(a) Probability that a random sample of n = 45 oil changes results in a sample mean time < 10 ​minutes i=0.0001.

(b) The mean oil-change time is 15.55 minutes.

Explanation:

Let us denote the sample mean time as x

From the Then x = mean time = 16.2 minutes

The given standard deviation = 3.4 minutes

The value of n sample size = 45

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION