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
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