Question

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 60. You also happen to know that the distribution of scores on Professor Fisher’s final is approximately normal with a mean of 74 and a standard deviation of 7 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) Which Professor gives a higher proportion of F’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 69 and a standard deviation of 9, how high does your score have to be to earn an A?

Answer 1

a) Sketch is given below

b) Let X be the score on Professor Fisher's final

then

From z table , P(z>2.29) = 0.0110

Thus , proportion of students gets A on Professor Fisher's final = 0.0110

Let Y be the score on Professor Savage's final

then

From z table , P(z>2.29) = 0.2514

Thus , proportion of students gets A on Professor Savage's final = 0.2514

Therefore , Professor Savage gives higher proportion of A's

(b)

From z table , P(z>-2) = 0.0227

Thus , proportion of students gets F on Professor Fisher's final = 0.0227

From z table , P(z<-1) = 0.1587

Thus , proportion of students gets F on Professor Savage's final = 0.1587

Therefore , Professor Savage gives higher proportion of F's

(d)

Let M be the score on Professor Fisher's final

then

We have to find c such that

P(M>c) =0.10

From z table , P(z> 1.29) =0.10

The score have to at least 80.61 to score A