Question

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

A: Top 13%13% of scores

B: Scores below the top 13%13% and above the bottom 56%56%

C: Scores below the top 44%44% and above the bottom 21%21%

D: Scores below the top 79%79% and above the bottom 9%9%

F: Bottom 9%9% of scores

Scores on the test are normally distributed with a mean of 79.779.7 and a standard deviation of 8.48.4.

Answer 1

Let X follows normal distribution with mean = = 79.7 and standard deviation = 8.4

A) Top 13% of scores

THat is P( Z > z) = 0.13

This implies P(Z < z) = 1 - 0.13 = 0.87

Let's used minitab:

Step 1: Click on Graph >>> Probability Distribution Plot ...

Select View Probability and then click on OK

Fill the necessary information in the box

Look the following image:

Then select Shade Area and fill the necessary information:

Look the following image:

Then click on OK so we get the following output

Fro this output we conclude that the Top 13% area is above 89.16

B) Scores below the top 13% and above the bottom 56%

Step 1: Click on Graph >>> Probability Distribution Plot ...

Select View Probability and then click on OK

Fill the necessary information in the box

Look the following image:

Then select Shade Area and fill the necessary information:

that is Select Left Tail and fill 0.56 in Probability Box

Look the following image:

Then click on OK so we get the following output

So that from Part A and the above output we conclude that

the Top 13% area is above 89.16 and above the bottom score is 80.97