Refer to Exercise 51.

a. Assume that F and M are independent random variables. Explain what this means in context.

b. Calculate and interpret the standard deviation of the difference D = F − M in their scores.

c. From the information given, can you find the probability that the randomly selected female student has a higher SSHA score than the randomly selected male student? Explain why or why not.

Exercise 51.

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures academic motivation and study habits. The SSHA score F of a randomly selected female student at a large university has mean 120 and standard deviation 28, and the SSHA score M of a randomly selected male student at the university has mean 105 and standard deviation 35. Suppose we select one male student and one female student at random from this university and give them the SSHA test. Calculate and interpret the mean of the difference D = F − M in their scores.