In a recent study of medical students it was found that medi

In a recent study of medical students, it was found that medical residents\' average number of hours worked per week was 81.7. The number of hours worked per week by medical residents is approximately normally distributed with a standard deviation of 6.9 hours.

A.) What is the probability that a randomly selected resident works more than 80 hours per week?

B.) What is the probability that a randomly selected resident works more than 100 hours per week?

C.) If a sample of 16 medical students selected, what is the probability that the probability that the mean number of hours worked by then members of that sample is more than 80 hours per week?

Solution

A)

z = (80 - 81.7)/6.9 = -0.25

Probability (X>80) = 1 - 0.4013 = 0.5987 Answer

B)

z = (100 - 81.7)/6.9 = 2.65

Probability (X>80) = 1 - 0.9960= 0.004 Answer

C)

z = (80 - 81.7)/(6.9/sqrt(16)) = -0.99

Probability (X>80) = 1 - 0.1611 = 0.8389 Answer