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 X
the sample average tensile strength of a random sample of 40 type-A specimens, and let Y
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(1  X  Y  1).

d. Calculate P(X  Y  10). If you actually observed X  Y  10, would you doubt that 1  2
5?