Question

consider grading an exam on curve where it is decided ahead of time that certain percentage of the class will earn A's, a certain percentage B's, and so on. Suppose the exam scores for a large chemistry class are normally distributed with a mean of 68 and a standard deviation of 14.

1. if the top 10% of the scores are given a grade A, what is the minimum score required to earn an A?

2. If the next 25% of the scores are given a grade of B, what is the minimum score required to earn a B?

3. If only the bottom 10% of the score are given a failing grade, what is the minimum score required to pass?

Answer 1

let X is score so X is normal with mean =68 SD=14

1)

let for grade A minimum marks required is "a" then

P(X>a) =0.1

now

from Z table P(Z>1.28)=0.1 So

2)

let required marks for grade "B' is b then

P(b<X<a) =P(b<X<85.92)=0.25

now

from Z table P(Z<0.385)=0.65 so

c)

let the required mark is "f" then

P(X<f) =0.1

now

from Z table P(Z<-1.28) =0.1

so