In a recent year, there were approximately 250,000,000 registered motor vehicles in the United States. Of these, approximately 4% were involved in an accident during the year. Assume that a simple random sample of n = 200 vehicles is drawn. Use the Poisson approximation to the binomial distribution to compute the following:

a. The probability that exactly six of the 200 vehicles were involved in an accident

b. The probability that fewer than three of the 200 vehicles were involved in an accident

c. The probability that more than 10 of the 200 vehicles were involved in an accident

d. The mean number of vehicles that were involved in an accident

e. The standard deviation of the number of vehicles that were involved in an accident