Question

A humanities professor assigns letter grades on a test according to the following scheme. A: Top 6% of scores B: Scores below the top 6% and above the bottom 59% C: Scores below the top 41% and above the bottom 17% D: Scores below the top 83% and above the bottom 7% F: Bottom 7% of scores Scores on the test are normally distributed with a mean of 79 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.

Answer 1

Limits for B scores

( 79,2 ; 92 )

Explanation:

The interval we are looking for is between 6 % and 59%

p₁ = 6 % p₁ = 0,06

As this point is at the right tail of the bell we better look for

p = 1- 0,06 p = 0,94

In z-table z score for 0,94062 is: z₁ = 1,56 ( 0,94062 ≈ 0,94 )

Doing the same to find z₂ score for 59% or 0,59

In z-table again

p = 0,59

z₂ = 0,023

Now we know

1,56 * σ = x₁ - 79

1,56*8,4 + 79 = x₁

x₁ = 92,10 or x₁ = 92

And

0,023*8,4 + 79 = x₂

x₂ = 79,19 or x₂ = 79,2