A student who usually does very poorly in math is trying to decide whether to take Professor A or Professor B for statistics. The two professors have similar teaching styles and the same grading policies. Last semester, the distribution of Professor A’s students’ scores on all tests had mean 80% and standard deviation 10%, and the distribution of Professor B’s students’ scores on all tests had mean 80% and standard deviation 3%.
a. With which professor would the student probably get higher test scores? Explain.
b. Is it possible the student would actually get higher tests scores with the other professor? Give at least two reasons why or why not.