Question

A math professor notices that scores from a recent exam are normally distributed with a mean of 72 and a standard deviation of 5.

(a) What score do 75% of the students exam scores fall below?
Answer:

(b) Suppose the professor decides to grade on a curve. If the professor wants 2.5% of the students to get an A, what is the minimum score for an A?
Answer:

Answer 1

Given,

= 72 , = 5

We convert this to standard normal as

P(X < x) = P(Z < ( x - ) / )

We have to calculate x such that

P(X < x) = 0.75

From Z table, z-score for the probability of 0.75 is 0.6745

( x - ) / = 0.6745

( x - 72) / 5 = 0.6745

x = 75.37

b)

We have to calculate x such that P(X > x) = 0.025

P(X < x) = 1 - 0.025

P(X < x) = 0.975

P(Z < ( x - ) / ) = 0.975

From Z table, z-score for the probability of 0.975 = 1.96

( x - ) / = 1.96

( x - 72) / 5 = 1.96

x = 81.8