Question

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

A: Top 14%14% of scores

B: Scores below the top 14%14% and above the bottom 57%57%

C: Scores below the top 43%43% and above the bottom 24%24%

D: Scores below the top 76%76% and above the bottom 8%8%

F: Bottom 8%8% of scores

Scores on the test are normally distributed with a mean of 69.669.6 and a standard deviation of 99. Find the numerical limits for a D grade.

HOW DO I SOLVE IT ON TI-84PLUS

Answer 1

Solution:

Given:

A: Top 14% of scores

B: Scores below the top 14% and above the bottom 57%

C: Scores below the top 43% and above the bottom 24%

D: Scores below the top 76% and above the bottom 8%

F: Bottom 8% of scores

Scores on the test are normally distributed with a mean of 69.6 and a standard deviation of 9.

We have to find the numerical limits for a D grade.

We have D: Scores below the top 76% and above the bottom 8%

So Area for D is : = 100% - (bottom % + top %) = 100% - ( 8% +76%) = 100% - 84% = 16% = 0.16

Thus total area below lower limit of D = 8% = 0.08 and

total area upper limit of D = 8% + 16% = 24% = 0.24

Now use following steps in TI 84: ( Note to get each area we use same formula used above)

Press 2ND and invNorm(

Enter numbers:

Area = 0.08

Click on Paste and press Enter two times.

Lower limit for D grade = 56.95

Use same steps above to get upper limit

Enter Area = 0.24

Upper limit = 63.24

Thus the numerical limits for a D grade are: 56.95 and 63.24