Question: Study habits The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures academic motivation and study habits. The distribution of SSHA scores among the women at a college has mean 120 and standard deviation 28, and the distribution of scores among male students has mean 105 and standard deviation 35. You select a single male student and a single female student at random and give them the SSHA test.
(a) Find the mean and standard deviation of the difference (female minus male) between their scores. Interpret each value in context.
(b) From the information given, can you find the probability that the woman chosen scores higher than the man? If so, find this probability. If not, explain why you cannot.