Question

A large group of students took a test in physics and the final grades have a mean of 70 with a standard deviation of 10. If the graph of the scores has normal distribution, what percentile would a student be in if they earned an A on the test? (A is a score greater than or equal to 90)

50th percentile

2nd percentile

48th percentile

98th percentile

Answer 1

Answer: 98th percentile (choice D)

Work Shown:

x = 90 = raw score

mu = 70 = mean

sigma = 10 = standard deviation

z = (x-mu)/sigma

z = (90-70)/10

z = 2

The score of x = 90 is exactly 2 standard deviations above the mean 70.

Then use the Empirical Rule chart as shown below. Notice how roughly 95% of the normal distribution is within 2 standard deviations of the mean. That leads to 100-95 = 5% in both tails combined and 5/2 = 2.5% in each tail.

Having 2.5% in the upper tail indicates 100-2.5 = 97.5% of the area is to the left of z = 2. The 97.5% rounds to 98%.

Therefore, we're in the 98th percentile. Roughly 98% of the grades are below an A (of 90 or better).