Chapter 5.3, Problem 5.32ACI

Rental car fleet evaluation. National Car Rental Systems, Inc., commissioned the U.S. Automobile Club (USAC) to conduct a survey of the general condition of the cars rented to the public by Hertz, Avis, National, and Budget Rent-a-Car.* USAC officials evaluate each company’s cars using a demerit point system. Each car starts with a perfect score of 0 points and incurs demerit points for each discrepancy noted by the inspectors. One measure of the overall condition of a company’s cars is the mean of all scores received by the company (i.e., the company’s fleet mean score). To estimate the fleet mean score of each rental car company, 10 major airports were randomly selected, and 10 cars from each company were randomly rented for inspection from each airport by USAC officials (i.e., a sample of size n = 100 cars from each company’s fleet was drawn and inspected).

* Information by personal communication with Rajiv Tandon, corporate vice president and general manager of the Car Rental Division, National Car Rental Systems, Inc., Minneapolis, Minnesota.

1. a. Describe the sampling distribution of $\bar{x}$, the mean score of a sample of n = 100 rental cars.
2. b. Interpret the mean of $\bar{x}$ in the context of this problem.
3. c. Assume µ = 30 and σ = 60 for one rental car company. For this company, find $P\left(\bar{x}\ge 45\right)$.
4. d. Refer to part c. The company claims that their true fleet mean score “couldn’t possibly be as high as 30.” The sample mean score tabulated by USAC for this company was 45. Does this result tend to support or refute the claim? Explain.