the head of maintenance at xyz rent-a-car believes that the mean number of miles between services is 4639 miles, with a standard deviation of 437 miles. if he is correct, what is the probability that the mean of a sample of 32 cars would be less than 4424 miles? round your answer to four decimal places.

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25-10-2022
Mathematics

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the head of maintenance at xyz rent-a-car believes that the mean number of miles between services is 4639 miles, with a standard deviation of 437 miles. if he is correct, what is the probability that the mean of a sample of 32 cars would be less than 4424 miles? round your answer to four decimal places.

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Parrain Parrain · Answer 1 · 2022-10-27T14:39:59-04:00

Based on the mean miles between the services and the standard deviation, the probability that the mean of 32 cars as a sample would be less than 4,424 miles is 0.0027.

How to find the probability?

The required probability is for the possibility that in a sample of 32 cars, the number of services would be less than 4,424.

The probability can be found by the formula:

P (x < 4,424) = P ( Z < (4,424 - 4,639) / (437 / √32))

This gives us:
P (x < 4,424) = P ( Z < -2.78)

Using the Z table shows that the probability would be 0.0027.

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