Question

In: Statistics and Probability

An automotive repair shop has determined that the average service time on an automobile is 2...

An automotive repair shop has determined that the average service time on an automobile is 2 hours with a standard deviation of 30 minutes. A random sample of 36 services is selected. (a) What is the probability that the sample of 36 will have a mean service time greater than 115 minutes? (b) Assume the population consists of 400 services. Determine the standard error of the mean.

Solutions

Expert Solution

Solution:

Given: An automotive repair shop has determined that the average service time on an automobile is 2 hours with a standard deviation of 30 minutes.

For two hours, number of minutes = 2 X 60 = 120 minutes.

Thus Mean number of minutes = = 120 and standard deviation =

Sample size = n = 36

Part a) Find the probability that the sample of 36 will have a mean service time greater than 115 minutes

That is:

Find z score :

Thus we get:

Look in z table for z = -1.0 and 0.00 and find area.

P( Z < -1.00) = 0.1587

Thus

Thus the probability that the sample of 36 will have a mean service time greater than 115 minutes is 0.8413

Part b) the population consists of 400 services. That is : n = 400

We have to determine the standard error of the mean.

It is given by formula:

Thus the standard error of the mean is

orchestra answered 1 year ago

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