Question

Students’ scores on a test in a public administration course follow a normal distribution with a mean of 150 points and a standard deviation of 12. One student who scored 161 on the test and received the grade of B is considering protesting his grade. He feels that the professor did not like him and awarded him a lower grade than his score deserved. The professor disagrees: She maintains that the top 10 percent of scores were given an A, the next 10 percent a B and so on—and that there was no discrimination. Based on the professor’s grading criteria, does the student have grounds for protest? Explain your answer.

Answer 1

X: Students’ scores on a test in a public administration

X  follow a normal distribution with a mean of 150 points and a standard deviation of 12

Let X_B be the minimum score to give a "B' grade

Given,

top 10 percent of scores were given an A, the next 10 percent a B

i.e 20% student get a score more than X_B

i,e

P(X>X_B) = 20/100 =0.20

P(X>X_B) =1 - P(XX_B) = 0.20 ; P(XX_B)=1-0.20 = 0.80

Z_B : Z-score for X_B

Z_B = (X_B - mean)/standard deviation = (X_B -150)/12 ;

X_B = 150+ 12Z_B

Also,

P(ZZ_B) = P(XX_B) = 0.80;

From standard normal tables,

P(Z0.84) = 0.7995

Z_B = 0.84

X_B = 150+ 12Z_B = 150 + 12 x 0.84 = 10.08 =160.08

Therefore minimum score required to get a B = 160.08

As the student  scored 161 > 160.08 : Minimum score required to get B on the test ; the student does have grounds for protest