Question: 28 A study of rush hour traffic in San Francisco counts the number of people in each car entering a freeway at a suburban interchange. Suppose that this count has mean 1.5 and standard deviation 0.75 in the population of all cars that enter at this interchange during rush hours.

a) Could the exact distribution of the count be Normal? Why or why not?

b) Traffic engineers estimate that the capacity of the interchange is 700 cars per hour. According to the central limit theorem, what is the approximate distribution of the mean number of persons \(\bar{X}\) in 700 randomly selected cars at this interchange?

c) What is the probability that 700 cars will carry more than 1075 people? (Hint: Restate this event in terms of the mean number of people (xbar) per car)