Suppose the expected tensile strength of type-A steel is105ksi and the standard
Chapter 5, Problem 73(choose chapter or problem)
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 \(\bar X\) = the sample average tensile strength of a random sample of 40 type-A specimens, and let \(\bar Y\) = the sample average tensile strength of a random sample of 35 type-B specimens.
a. What is the approximate distribution of \(\bar X\)? Of \(\bar Y\)?
b. What is the approximate distribution of \(\bar X - \bar Y\)? Justify your answer.
c. Calculate (approximately) \(P(-1 \leq \bar X - \bar Y \leq 1)\).
d. Calculate \(P(\bar X - \bar Y \geq 10)\). If you actually observed \(\bar X - \bar Y \geq 10\), would you doubt that \(\mu_1 - \mu_2 = 5\)?
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