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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 4764 miles, with a variance of 193,600. If he is correct, what is the probability that the mean of a sample of 34 cars would differ from the population mean by less than 149 miles? Round your answer to four decimal places.

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that,

mean = = 4764

variance = 193600

standard deviation = = 440

n = 34

= 4764

= / n = 440 / 34

= P[-149 / 440 / 34 < ( - ) / < 149 / 440 / 34)]

= P(-1.97 < Z < 1.97)

= P(Z < 1.97) - P(Z < -1.97)

= 0.9756 - 0.0244

= 0.9512

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