The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 4959 miles, with a standard deviation of 448.If he is correct, what is the probability that the mean of a sample of 43 cars would differ from the population mean by less than111 miles? Round your answer to four decimal places.

0.8958

Step-by-step explanation:

Given that:

The mean = 4959

The standard deviation = 448

The sample size n = 43

By applying the central limit theorem;

The purpose of this question is to calculate the probability that the mean of a sample of 43 cars would differ from the population mean by less than111 miles.

This implies that;

= P ( Z < 1.627 ) - P(Z < -1.627)

From the standard normal tables

= 0.94791 -0.05208

= 0.89583

≅ 0.8958  to four decimal places.