Students\' scors on my first test follow a normal distribution with a mean of 15

Question

Students' scors on my first test follow a normal distribution with a mean of 150 points and a standard devation of 12. One student who scored 145 on the test received a F letter grade is very upset and is considering protesting his grade to the MPA director. He feels I awarded him a lower grade for personal reasons. I maintain that grades were given out in increments of 10% with the top 10% of the scores receiving an A.

A. Based on my grading criteria, what numerical score did the student receive on the exam?

B.Given the information provide above, what percentage of the students received a higher score that the student?

C. The MPA directos is planning a talk to the student and he wants to know the lowest score the student could have earned in order to recieve a C grade?

D. What is the lowest score the disgruntled student could have earned and still receive a B?

Explanation / Answer

A.

Z value for X = 145 is

Z = (X - mean)/std dev = (145 - 150)/12 = -0.4167

Using Z table,

P(X = 145) = P(Z = -0.4167) = 0.366

If the numerical score is between 0 - 10, the numerical score of the student is 3.66.

B.

P(X > 145) = P(Z > -0.4167) = 0.6615

So, 66.15% of the students received a higher score that the students.

C.

In order to receive C grade, 30% of scores are higher than the the student score.

So, P(X > x) = 0.3

Z value for p= 0.3 is 0.5244

Therefore, (X-150)/12 = 0.5244

=> X = 150 + 12*0.5244 = 156.29

So, the lowest score to recieve a C grade is 156.3

D.

In order to receive B grade, 20% of scores are higher than the the student score.

So, P(X > x) = 0.2

Z value for p= 0.2 is 0.8416

Therefore, (X-150)/12 = 0.8416

=> X = 150 + 12*0.8416 = 160.1

So, the lowest score to recieve a B grade is 160.1

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