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% C: Scores below the top 39% and above the bottom 20% D: Scores below the top 80% and above the bottom 10% F: Bottom 10% of scores Scores on the test are normally distributed with a mean of 72.8 and a standard deviation of 7.3. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.

Solution :

The test is distributed normally with mean of 72.8 and the standard deviation of 7.3

Finding numerical limits for the D grade.

D grade : Scores below the top 80% and above the bottom 10%.

Let the bottom limit for D grade be and the top limit for D grade be .

First find the bottom numerical limit for a D grade is :

   ..........(1)

From (1)

      = 63.45

       ≈ 64

Now the top numerical limit for D grade :

   ..........(2)

From (2)

      = 66.668

       ≈ 67

Therefore, the numerical limit for a D grade is 64 to 67.

step-by-step explanation:

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