Answer to Question #330846 in Statistics and Probability for hale

Question

The scores for a mathematics course seem to be normally distributed with mean 70 & standard deviation of 8. If the instructor wishes to give an A grade to 10% of the students, what should be the dividing line between an A grade and a B grade?

Answer 1

Let's find the 90th percentile; the closest value in z-table is 0.8997, it corresponds to z = 1.28.

So,

$P(Z<1.28) =0.8997\approx0.9,\\ P(Z>1.28)\approx1-0.9=0.1,\\ z=\cfrac{x-\mu} {\sigma}, \\ x=z\sigma+\mu=1.28\cdot8+70=80.24.$

Thus, 80 should be the dividing line between an A grade and a B grade.