Question

On a test that has a normal distribution, a score of 30 falls three standard deviations below the mean, and a score of 60 falls three standard deviations above the mean. Determine the mean of this test.

Answer 1

• 45

Explanation:

Let μ - mean, σ - standard deviation.

Given:

A score of 30 falls three standard deviations below the mean:

• μ - 3σ = 30

A score of 60 falls three standard deviations above the mean:

• μ + 3σ = 60

Add up the two expressions and find the value of μ:

• μ - 3σ + μ + 3σ = 30 + 60
• 2μ = 90
• μ = 45

The mean is 45