Question: J.D. Power and Associates calculates and publishes various statistics concerning car quality. The initial quality score measures the number of problems per new car sold. For 2004 model cars, the Lexus had 0.87 problems per car. Korea s Kia had 1.53 problems per car (D. Hakim, Hyundai Near Top of a Quality Ranking, The New York Times, April 29, 2004, p. C8). Let the random variable X be equal to the number of problems with a newly purchased Lexus.
a. What assumptions must be made in order for X to be distributed as a Poisson random variable? Are these assumptions reasonable? Making the assumptions as in (a), if you purchased a 2004 Lexus, what is the probability that the new car will have
i. zero problems?
ii. two or less problems?
b. Give an operational definition for problem. Why is the operational definition important in interpreting the initial quality score?