A company publishes statistics concerning car quality. The initial quality score measures the number of problems per new car sold. For one year, Car A had 1.15 problems per car. Let the random variable X be equal to the number of problems with a newly purchased model A car. Complete parts (a) through (d). a. What assumptions must be made in order for X to be distributed as a Poisson random variable? Select all the assumptions for a Poisson distribution. A. The probability of a problem is the same for each period of time B. At least 30 model A cars are sold. LY C. The number of problems in a given period is independent of the number of problems in any other period. D. The probability of a problem in a time period approaches zero as the length of the time period becomes smaller. b. Making the assumptions as in (a), if you purchased a model A car, what is the probability that the new car will have zero problems? The probability that the new model A car will have zero problems is 0.3166. (Round to four decimal places as needed.) c. Making the assumptions as in (a), if you purchased a model A car, what is the probability that the new car will have two or fewer problems? The probability that a now model A car will have two or fewer problems is (Round to four decimal places as needed )