Question

An English professor assigns letter grades on a test according to the following scheme.

A: Top 13%of scores

B: Scores below the top
13% and above the bottom 61%61%6

C: Scores below the top 39% and above the bottom 22%

D: Scores below the top 78% and above the bottom 6%

F: Bottom 6% of scores

Scores on the test are normally distributed with a mean of 75.1 and a standard deviation of 9.1. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.

Answer 1

we have Scores below the top 78% and above the bottom 6%

Scores below top 78% means score below 22% from the bottom

using the online calculator at https://www.easycalculation.com/statistics/percentile-to-z-score.php

z score for below top 78% is -0.7722 and z score for above the bottom 6% is 1.5548

we have mean = 75.1 and SD = 9.1

now, we will calculate for the required numerical limits for a D grade

we have formula z = (x-mean)/sd

putting z = -0.7722, mean = 75.1 and SD = 9.1

we get

-0.7722 = (x-75.1)/9.1

multiplying both sides by 9.1, we get

-0.7722*9.1 = x - 75.1

-7.027 = x - 75.1

adding 75.1 on both sides, we get

-7.027 + 75.1 = x

or x = 68.073 or 68(rounded to nearest whole number)

Calculation for above the bottom 6%

we have formula z = (x-mean)/sd

putting z = 1.5548, mean = 75.1 and SD = 9.1

we get

1.5548 = (x-75.1)/9.1

multiplying both sides by 9.1, we get

1.5548*9.1 = x - 75.1

14.15 = x - 75.1

adding 75.1 on both sides, we get

14.15 + 75.1 = x

or x = 89.25 or 89 (rounded to nearest whole number)

so, the required numerical limits for a D grade is 68 to 89