Question

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

2020​-minute

​oil-change facility is unknown.​ However, records indicate that the mean time is

21.4 minutes21.4 minutes​,

and the standard deviation is

4.3 minutes4.3 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 less than or equal to 30.

B.

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

Your answer is correct.

C.

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

D.

Any sample size could be used.

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

=45 oil changes results in a sample mean time less than 20 ​minutes? The probability is approximately __________

Answer 1

Solution :

Given that ,

mean = = 21.4 minutes

standard deviation = = 4.3 minutes

n = 45

a) correct option is = B

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

=    = 21.4 minutes

= / n = 4.3 / 45 = 0.641

b) P( < 20) = P(( - ) / < (20 - 21.4) / 0.641)

= P(z < -2.18)

Using z table

= 0.0146