Question: A couple considering the purchase of a new home would like to estimate the average number of cars that go past the location per day. The couple guesses that the number of cars passing this location per day has a population standard deviation of 170.

a. On how many randomly selected days should the number of cars passing the location be observed so that the couple can be 99% certain the estimate will be within 100 cars of the true average?

b. Suppose the couple finds out that the population standard deviation of the number of cars passing the location per day is not 170 but is actually 272. If they have already taken a sample of the size computed in part a, what confidence does the couple have that their point estimate is within 100 cars of the true average?

c. If the couple has already taken a sample of the size computed in part a and later finds out that the population standard deviation of the number of cars passing the location per day is actually 130, they can be 99% confident their point estimate is within how much of the true average?