Question

1. A professor at a major university gives an exam to a large lecture class of several hundred students. The professor requires a minimum of 65 points on the test to pass, but within the range of passing, the professor will “curve” for the letter grades: A, B, or C. The exam grades are approximately normally distributed with a mean of 72.1 points and a standard deviation of 8.4 points.

(a) Compute the percent of students that pass the class; that is, the percent of students that receive 65 points or more.

(b) The professor will limit “A” to the top 8% of the class. Compute the point cut-off an “A.”

Answer 1

1)

Solution :

(a)

P(x 65) = 1 - P(x   65)

= 1 - P[(x - ) / (65 - 72.1) / 8.4]

= 1 -  P(z -0.85)  

= 0.8023

(b)

P(Z <1.405) = 0.92

Using z-score formula,

x = z * +

x = 1.40 * 8.4 + 72.1 = 83.86

the point cut-off an “A" = 83.86 points