2) 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).
a)describe the sampling distribution of x the mean score of a sample of n=1—rental cars .
b) interpret the mean of x in the context of this problem .
c) assume u= 30 and &= 60 for one rental car company. For this company , find p(x>45)
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 does this result tend to support or refute the claim ? explain