Suppose the expected tensile strength of type-A steel is 105 ksi and the standard deviation of tensile strength is 8 ksi. For type-B steel, suppose the expected tensile strength and standard deviation of tensile strength are 100 ksi and 6 ksi, respectively. Let the sample average tensile strength of a random sample of 40 type-A specimens, and let the sample average tensile strength of a random sample of 35 type-B specimens.

a. What is the approximate distribution of X? Of Y?

b. What is the approximate distribution of X- Y? Justify your answer.

c. Calculate (approximately) P(-1sX-Y 1).

d. Calculate PX-Y 10). If you actually observed X- Y 10, would you doubt that = 5?