Given data from a distribution having a mean of 20 and a standard deviation of 5, a random sample of 100 was taken. The sample mean was computed from this sample. What is the probability that the sample mean is less than 21.

About 75% of all heart transplants will survive for at least 3 years, 90 heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be less than 70%.

An ice cream company claims that the mean weight of its ice cream cartons is 10 oz with a standard deviation of 0.5 oz. Assume the weights are normally distributed. A random sample of 49 cartons are taken and the sample mean computed. What is the probability that the sample mean exceeds 10.2 oz.