Question

professor kingsfield's class follows very strict grading guidelines. Assume that student averages in Kingsfield's class are normally distributed with a mean of 62 points and a standard deviation of 12 points. Professor Kingsfield wants letter grades in his class to have a very specific distribution: 68 percent of students get Cs, 13.5 percent get Ds, 13.5 percent get Bs, 2.5 percent receive Fs, and the top 2.5 percent get As. What should be the numeric range for each letter grade?

Students with __ or above get As

Students with averages between __ and __ get Bs.

Students with averages between __ and __ get Cs.

Students with averages between __ and __ get Ds.

Students with __ or below get Fs.

Please show how you got the answers:)

Answer 1

Let the rv X denote student's score.

Then X~ N( 62,12) or we may write ,

Now , we know , for a standard normal distribution :

So,

For , grade A ,a student needs Z score of 2 or above .

SO, required score

For , grade B ,a student needs Z score between 1 and 2 .

SO, required score

For , grade C ,a student needs Z score between -1 and 1 .

SO, required score

For , grade D ,a student needs Z score between -2 and -1 .

SO, required score

and finally student with score less 44 gets F .