An analysis of the grades on the first test in History 101 r

An analysis of the grades on the first test in History 101 revealed that they approximate a normal curve with a mean of 78 and a standard deviation of 9. The instructor wants to award the grade of A to the upper 10 percent of the test grades. What is the dividing point between an A and a B grade?

Solution

P(X>c)=0.1

--> P((X-mean)/s <(c-78)/9)=1-0.1=0.9

--> P(Z<(c-78)/9) =0.9

--> (c-78)/9 =1.28 (from standard normal table)

So c= 78+1.28*9=89.52

Answer: 90