Question

The numerical course grades in a statistics course can be approximated by a normal model with a mean of 70 and a standard deviation of 10. The professor must convert the numerical grades to letter grades. She decides that she wants 10% A's, 30% B's, 40% C's, 15% D's, and 5% F's.

a. What is the cutoff for an A grade?

(Use 2 decimal places.) (Draw a picture!.)

a. What is the cutoff for an B grade?

(Use 2 decimal places.)

a. What is the cutoff for an C grade?

(Use 2 decimal places.)

a. What is the cutoff for an D grade?

(Use 2 decimal places.)

Answer 1

Solution:

We are given that grades are approximately normally distributed.

Mean = 70

SD = 10

a. What is the cutoff for an A grade?

Here, we have to find the cut-off for upper 10% grades (or lower 90%).

Z = 1.281552

(by using z-table)

X = Mean + Z*SD

X = 70 + 1.281552*10

X = 82.81552

Answer = 82.82

a. What is the cutoff for an B grade?

Z-score for upper (10+30) = 40% or lower 60% is given as below:

Z = 0.253347

(by using z-table)

X = Mean + Z*SD

X = 70 + 0.253347*10

X = 72.53347

Answer = 72.53

a. What is the cutoff for an C grade?

Z-score for upper (10+30 +40) = 80% or lower 20% is given as below:

Z = -0.84162

(by using z-table)

X = Mean + Z*SD

X = 70 + (-0.84162)*10

X = 61.5838

Answer = 61.58

a. What is the cutoff for an D grade?

Z-score for upper (10+30 +40 +15) = 95% or lower 5% is given as below:

Z = -1.64485

(by using z-table)

X = Mean + Z*SD

X = 70 + (-1.64485)*10

X = 53.5515

Answer = 53.55