Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation of 9. The teacher wants to give A’s to the top 10% of students, B’s to the next 25%, and C’s to the next 42%.

Question

Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation of 9. The teacher wants to give A’s to the top 10% of students, B’s to the next 25%, and C’s to the next 42%.
a.) what is the bottom cutoff for a C grade?
b.) what is the bottom cutoff for a B grade?
c.) what is the bottom cutoff for a A grade?
what is the correct formula for this?

PsyDAG · Answer

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities (.10, .35 & .77) and the corresponding Z scores. Insert into equation above.