Question

A sociology professor assigns letter grades on a test according to the following scheme. A: Top 9% of scores B: Scores below the top 9% and above the bottom 63% C: Scores below the top 37% and above the bottom 24% D: Scores below the top 76% and above the bottom 7% F: Bottom 7% of scores Scores on the test are normally distributed with a mean of 73.9 and a standard deviation of 9.9. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.

Answer 1

Answer:
Let U be the Mean and Sd be the standard deviation.
Mean U= 73.9
Standard deviation SD= 9.9
P(X < A) = P(Z < (A - U)/SD)
Let the lower limit for D be DL and upper limit for D be DU
P(X < DL) = 0.07
P(Z < (DL - 73.9)/9.9) = 0.07
Z value of -1.48 is 0.07 so we cn write that...
(DL - 73.9)/9.9) = -1.48
DL = 59
P(X > DU) = 0.76\
P(X < DU) = 1 - 0.76 = 0.24
P(Z < (DU - 73.9)/9.9) = 0.24
Z value of -0.71 is 0.24 so we cn write that...
(DU - 73.9)/9.9) = -0.71
DU = 67