42. For males the expected pulse rate is 70 per second and the standard deviation is 10 per second. For women the expected pulse rate is 77 per second and the standard deviation is 12 per second. Let  the sample average pulse rate for a random sample of 40 men and let  the sample average pulse rate for a random sample of 36 women.

a. What is the approximate distribution of ? Of ?

b. What is the approximate distribution of ?

Justify your answer.

c. Calculate (approximately) the probability

d. Calculate (approximately) . If you actually observed , would you doubt that m1  m27? Explain.