Question: An agricultural economist is interested in determining the average diameter of peaches produced by a particular tree. A random sample of 50 peaches is taken and the sample mean calculated. Suppose that the average diameter of peaches on this tree is known from previous years' production to be 75 millimeters with a standard deviation of 15 millimeters. What is the probability that the sample mean exceeds 78 millimeters?

(a) Referring to problem 1_3.5, what is the probability that the sample mean differs from the population mean by less than 2?

(b) Referring to problem 1_3.5, if the sample mean was actually 65, would you consider that unusual?