1. Suppose that you are deciding whether to take Professor Fisher's class or Professor Savage's class 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 on Professor Savage's final is approximately normal with mean 78 and standard deviation 18. (a) Identify which distribution is Professor Fishers's grades and which distribution is Professor Savage's grades. Justify your choice. 22 33 44 55 66 77 88 99 110 121 X English (United States) Focus E -fin: X l 2 3 4 5 6 {J}. 3' [b1 which professor gives the highest proportion of A's? [An A is 95 and abovei Show all work, including the calculator command. [cl Which professor gives the highest proportion of PS? {An F is 60 and below! Show all work, inclu ding the calculator command. [d} which professor passes more students? [Passing is a C, which is 10 and above: Show all work, inclu ding the calculator command. {e} What causes the differences you notice in parts [bi through {d}? Does it involve the mean or the standard deviation? Explain. 3 English (United States) :1 Focus E E, WEN\"... .5 {f} You decide to take Professor Fisher's class. Jusijfy your choice by using the appropriate parts of the analysis you just completed. [,3] You decide to take Professor Sauage's class. Jusijfy your choice by using the appropriate parts of the analysis you just completed. English [United States) 2. Suppose 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 nal turns out to be normal with a mean 59 and standard deviation 9, how high does your score have to be to earn an A? Support your answer with appropriate probability calculations, including the calculator command. 1mm [1 Focus E E, lX'L' 3 4 5 5 c5 ' 3. Suppose that Professors Wells and Zeddes have nal exam scores that are approximately normally distributed with mean 1'5. The standard deviation ofWells' scores is 10, and that of Zeddes' scores is 5. [a1 With which professor is a score of 90 more impressive? Support your answer with appropriate probability calculations, including the calculator command if applicable. [b1 Suppose you really want an A. Based on your answer above, which class would you take and why? 3 English (United States) {. J Focus E E
