Question

In: Statistics and Probability

The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services...

The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 2135 miles, with a variance of 145,924

.

If he is correct, what is the probability that the mean of a sample of 40 cars would differ from the population mean by less than 29 miles? Round your answer to four decimal places.

Solutions

Expert Solution

Solution :

Given that,

= / n = 382 / 40 = 60.3995

= P[(-29) /60.3995 < ( - ) / < (29) / 60.3995)]

= P(-0.48 < Z < 0.48)

= P(Z < 0.48) - P(Z < -0.48)

= 0.6844 - 0.3156

= 0.3688  

Probability = 0.3688


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