ROUNDED TO WHOLE NUMBER ANSWERS Last semester in the undergr

ROUNDED TO WHOLE NUMBER ANSWERS.

Last semester in the undergraduate course I was teaching I decided that I would curve the course and, thus, I had to determine where the break in grades would occur. One hundred students were enrolled in the course and the points earned were normally distributed with a mean of 500 and a standard deviation of 50. Therefore, what would the point total be that would separate:

a. A grade of F from D if the bottom 10% of the students was to receive a grade of F.

b. A grade of B from C if the top 30% of the students was to receive a grade of A or B.

Solution

(A) P(X<c)=0.1

--> P((X-mean)/s <(c-500)/50)=0.1

--> P(Z<(c-500)/50) =0.1

--> (c-500)/50= -1.28 (from standard normal table)

So c= 500-1.28*50=436

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(B) P(X>c)=0.3

--> P(Z<(c-500)/50) =1-0.3=0.7

--> (c-500)/50=0.52 (from standard normal table)

So c=500+0.52*50=526