1. ProfessorsGmdes Suppose 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 a final exam and F's to those scoring below {it}. You also happen to know that the disnibution of scores on Professor Fisher's final is approximately normal with a mean of T4 and a standard deviation of T and that the distribution of scores on Professor Savage's final is approximately normal with a mean of 78 and a standard deviation of 18. a) Produce a sketch of both teachers' grade distribution. b) Which Professor gives a higher proportion of A's? Show the calculations to support your answer. c) 1i.\"Jhich Professor gives a higher proportion of P's? Show the 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 a mean of 6'3 and a standard deviation of 9, how high does your score have to be to earn an A