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 2009 model cars, Ford had 1.02 problems per car and Dodge had 1.34 problems per car (data extracted from S. Carty, "U.S. Autos Power Forward with Gains in Quality Survey," USA Today, June 23, 2009, p. 3B). Let the random variable X be equal to the number of problems with a newly purchased 2009 Ford.
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 2009
Ford, what is the probability that the new car will have
b. Zero problems?
c. Two or fewer problems?
d. Give an operational definition for problem. Why is the operational definition important in interpreting the initial quality score?