Question

Assume that a set of test scores is normally distributed with a mean of 70 and a standard deviation of 10. In what percentile is a score of 65?

1. 95th
2. 79th
3. 46th
4. 30th

Answer 1

Given:
μ = 70, the mean
σ = 10, the standard deviation

The random variable is x = 65.
Calculate the z-score.
z = (x - μ)/σ = (65 -70)/10 = - 0.5

From standard ables, obtain
P(x<5) = 0.3085 ≈ 30%
The score of 65 is in the 30th percentile.

Answer: 30th