Question #330846

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?


1
Expert's answer
2022-04-20T13:51:03-0400

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)=0.89970.9,P(Z>1.28)10.9=0.1,z=xμσ,x=zσ+μ=1.288+70=80.24.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.


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