3. 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 aver- age 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-F? Justify your answer. Calculate (approximately) P(-1X-Y 1). d. Calculate PX-10). If you actually observed X-F 10, would you doubt that -p=5?