Question

(1 pt) A math professor notices that scores from a recent exam are normally distributed with a mean of 65 and a standard deviation of 8. Answer the following questions using integer values. (a) What score do 25% 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

Solution :

Given that ,

mean = = 65

standard deviation = = 8

a)

The z - distribution of the 25 % is,

P( Z < z ) = 25%

P( Z < z ) = 0.25

P( Z < -0.67 ) = 0.25

z = -0.67

Using z - score formula,

X = z * +

= -0.67 * 8 + 65  

= 59.64

The 25 % value is 59.64

b)

The z - distribution of the 2.5 % is,

P( Z < z ) = 2.5%

P( Z < z ) = 0.025

P( Z < -1.96 ) = 0.025

z = -1.96

Using z - score formula,

X = z * +

= -1.96 * 8 + 65  

= 49.32

The minimum score of an A is  49.32