For men, pulse rates (in beats per minute) are normally distributed with mean 70 and standard deviation 10. Women’s pulse rates are normally distributed with mean 77 and standard deviation 12. Let X̅ = the sample average pulse rate for a random sample of 40 men and let Y̅ = the sample average pulse rate for a random sample of 36 women.

a. What is the distribution of X̅ ? Of Y̅?

b. What is the distribution of X̅ – Y̅? Justify your answer.

c. Calculate P(–2 ≤ X̅ – Y̅ ≤ 1).

d.

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Calculate P(X-Y≤-15). actually observed X - Y you doubt that μ₁ −μ₂ = -7? Explain. If you -15, would