5. Suppose that you are deciding whether to take Professor Fisher's class or Professor Savage's next semester. You happen to know that each professor gives A's to those scoring above 90 on the final exam and F's to those scoring below 60. You also happen to know that the distribution of scores on Professor Fisher's final is approximately normal with mean 74 and standard deviation 7 and that the distribution of scores of Professor Savage's final is approximately normal with mean 78 and standard deviation 18. a. Produce a sketch of both teachers' grade distributions, on the same scale. b. Which professor gives the higher proportion of A's? Show the appropriate calculations to support your answer. c. Which professor gives the higher proportion of F's? Show the appropriate calculations to support your answer. d. Suppose that Professor DeGroot has a policy of giving A's to the top 10% of the scores on his final, regardless of the actual scores. If the distribution of scores on his final turns out to be normal with mean 69 and standard deviation 9, how high doe your score have to be to earn an A?