An analysis of the grades on the first test in History 101 revealed that they approximate a normal curve with a mean of 75 and a standard deviation of 8. The instructor wants to award the grade of A to the upper 10% of the test grades. To the nearest percent,what is the dividing point between an A and a B grade?
A)80
B)85
C)90
D)95

Question

Quizplus · Accepted Answer

Using a normal distribution table or calculator, we can find that the z-score corresponding to the upper 10% of the distribution is approximately 1.28. We can then use the formula z = (x - μ) / σ to solve for the corresponding test score, x, when μ = 75 and σ = 8, as follows:
1.28 = (x - 75) / 8
x - 75 = 10.24
x = 85.24
Rounding to the nearest percent, the dividing point between an A and a B grade would be 85%. Therefore, the best choice is B.

An Analysis of the Grades on the First Test in History