1. A vending machine advertises that its cups contain, on average, 12 ounces of coffee with standard deviation 0.4 ounce. Suppose that the company's advertisement is true.

a) Calculate the probability that a single randomly selected cup contains 11.5 ounces or less. If this calculation is not possible, explain why.
b) An inspection of an SRS of 50 cups from the vending machine is made to calculate the
sample mean . What are the mean and standard deviation of the sampling distribution
of 7 for the samples of size n=50?
c) The inspection yields a sample mean x~= 11.9 ounces. Calculate the probability that a random sample of 50 cups produces a sample mean of 11.5 ounces.