Question

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.

a. 0.6930
b. 0.7542
c. 0.8216
d. 0.8907

Answer 1

1) The probability that the mean of a sample of 40 cars would differ from the population mean by less than 29 miles is 0.7542 (Option b).

2) This is calculated using the standard normal distribution and the properties of the normal curve.

Step-by-step explanation:

1) To find the probability, we use the standard normal distribution and the formula for the standard error of the mean. With a known variance of 145,924 and a sample size of 40, the standard error is calculated as √(145,924/40). We then find the z-score for a difference of 29 miles and look up the corresponding probability.

2) The calculated probability of 0.7542 corresponds to the likelihood that the mean of a sample of 40 cars would differ from the population mean by less than 29 miles, given the provided variance and sample size.