Question

A large group of students took a test in Physics and the final grades have a mean of 70 and a standard deviation of 10. If we can approximate the distribution of these grades by a normal distribution, between what two scores of the test in the middle 95%?

Answer 1

The scores are between 50 and 90

Explanation:

When we say middle 95%, we means that this value falls between 2 standard deviations of the mean i.e

μ ± 2σ

Hence,

mean of 70 and a standard deviation of 10

μ ± 2σ

μ - 2σ

70 - (2 × 10)

= 70 - 20

= 50

μ + 2σ

= 70 + (2 × 10)

= 70 + 20

= 90