Question

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?
Select one:
a. 80
b. 85
c. 90
d. 95

Answer 1

Answer:

b. 85

Step-by-step explanation:

Average grade (μ) = 75

Standard deviation (σ) = 8

Assuming a normal distribution, the z-score corresponding to the upper 10% of the test grades is z = 1.28.

The minimum grade 'X' within the top 10% is given by:

$z=\frac{X-\mu}{\sigma}\\1.28=\frac{X-75}{8}\\X=85.24$

Rounding to the nearest percent, the dividing point between an A and a B grade is 85.