Suppose that, for a certain exam, a teacher grades on a curve according to the figure shown below. It is known that the grades follow a normal distribution with a mean of 60 and a standard deviation of 4. There are 45 students in the class. What score would be necessary to obtain a B?
A) 69
B) 60
C) 56
D) 64
E) 80

Question

Suppose that, for a certain exam, a teacher grades on a curve according to the figure shown below. It is known that the grades follow a normal distribution with a mean of 60 and a standard deviation of 4. There are 45 students in the class. What score would be necessary to obtain a B? 
A) 69 
B) 60 
C) 56 
D) 64 
E) 80

Quizplus · Accepted Answer

First, we need to find the z-score corresponding to a B grade. From the curve, we see that a B grade corresponds to the 65th percentile, which means that 65% of the class scored below the B grade and 35% of the class scored above the B grade. Using a standard normal table or calculator, we can find the z-score that corresponds to the 65th percentile, which is approximately 0.385.

Next, we use the z-score formula to find the corresponding raw score:
z = (x - mu) / sigma
0.385 = (x - 60) / 4
x - 60 = 1.54
x = 61.54

Therefore, a score of 61.54 is necessary to obtain a B, which rounds to 64. So the answer is D.

Suppose That, for a Certain Exam, a Teacher Grades on a Curve