Suppose the expected tensile strength of type-A steel is 105 ksi and the standard deviation of tensile

Question:

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 of ? Of ?
b. What is the approximate of X 2 Y? Justify your answer.
c. Calculate (approximately) P(-1 ≤ - ≤ 1).
d. Calculate P(X 2 Y $ 10). If you actually observed - ≥ 10, would you doubt that µ1 - µ2 = 5?
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