Question

An English professor assigns letter grades on a test according to the following scheme. A: Top 5% of scores B: Scores below the top 5% and above the bottom 64% C: Scores below the top 36% and above the bottom 23% D: Scores below the top 77% and above the bottom 9% F: Bottom 9% of scores Scores on the test are normally distributed with a mean of 78.8 and a standard deviation of 7.1 . Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.

Answer 1

Let X be the score on the test

X~ N( 78.8, 7.1²)

D: Scores below the top 77% and above the bottom 9%

Lower limit for D grade

P( Z < z ) = 0.09

P( Z < - 1.341) = 0.09 ( from the percentile table)

z = -1.341

= - 1.341

= -1.341

x= 78.8 - (7.1 * 1.341)

x= 69.28 i.e 69

Upper Limit For D grade

P( Z >z )= 0.77

P( Z < z) = 0.23

P( Z < - 0.739) = 0.23 ( from the percentile table)

z = -0.739

= - 0.739

= -0.739

x= 78.8 - (7.1 * 0.739)

x= 73.5531 i.e, 74

SO , D WILL BE GIVEN FOR THE SCORE BETWEEN 69 TO 74