A) The number of customers who enter a supermarket each hour is normally distributed with a mean of 600 and a standard deviation of 200. The supermarket is open 16 hours per day. What is the probability that the total number of customers who enter the supermarket in one day is greater than 10,000? (Hint: Calculate the average hourly number of customers necessary to exceed 10,000 in one 16-hour day.)

B) The manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 6.05 ounces and a standard deviation of .18 ounces. Suppose that you draw a random sample of 36 cans.

a. Find the probability that the mean weight of the sample is less than 5.97 ounces.

b. Suppose your random sample of 36 cans of salmon produced a mean weight that is less than 5.97 ounces. Comment on the statement made by the manufacturer.

C) The amount of time spent by North American adults watching television per day is normally distributed with a mean of 6 hours and a standard deviation of 1.5 hours.

a. What is the probability that a randomly selected North American adult watches television for more than 7 hours per day?

b. What is the probability that the average time watching television by a random sample of five North American adults is more than 7 hours?

c. What is the probability that, in a random sample of five North American adults, all watch television for more than 7 hours per day?

D) The marks on a statistics midterm test are normally distributed with a mean of 78 and a standard deviation of 6.

a. What proportion of the class has a midterm mark of less than 75?

b. What is the probability that a class of 50 has an average midterm mark that is less than 75?

E) The number of pizzas consumed per month by university students is normally distributed with a mean of 10 and a standard deviation of 3.

a. What proportion of students consume more than 12 pizzas per month?

b. What is the probability that in a random sample of 25 students more than 275 pizzas are consumed?