Surveys indicate that 60% of the vehicles in some metropolitan areas operate below peak performance, causing excessive emissions of pollutants. Transport Canada inspected 100 randomly selected vehicles in one of these areas.

a. Predict how closely a normal approximation will agree with the binomial calculation of the probability that exactly half of these vehicles cause unnecessary pollution.

b. Use the normal approximation to calculate the probability that exactly half of the vehicles inspected cause unnecessary pollution.

c. Use the formula for binomial probabilities to calculate the probability that exactly half of the vehicles inspected cause unnecessary pollution.

d. Do these calculations support your prediction in part a)? Explain why or why not.