Question

The shape of the distribution of the time required to get an oil change at a

20 -minute oil-change facility is unknown. However, records indicate that the meantime is 21.2 minutes, and the standard deviation is 3.4 minutes

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

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

nequals=40 oil changes results in a sample mean time less than 20 minutes?

(a) 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 less than 30.

D.

The sample size needs to be greater than 30.

Your answer is correct.

(b) The probability is approximate???

(Round to four decimal places as needed.)

Answer 1

Given that, Mean = 21.2 minutes

standard deviation = 3.4 minutes

a)  To compute probabilities regarding the sample mean using the normal model, the sample size needs to be greater than 30.

b) Given that, sample size ( n ) = 40

we want to find,

Answer: 0.0129