Question

On a test that has a normal distribution, a score of 48 falls two standard deviations

above the mean, and a score of 28 falls two standard deviations below the mean.
Determine the mean of this test.

Answer 1

To determine the mean of the test, we can use the information given about the scores falling two standard deviations above and below the mean.

Let's denote the mean of the test as μ and the standard deviation as σ.

We are given:
48 falls two standard deviations above the mean, so 48 = μ + 2σ.
28 falls two standard deviations below the mean, so 28 = μ - 2σ.

To solve for the mean μ, we can set up a system of equations with these two equations:

48 = μ + 2σ
28 = μ - 2σ

Adding the two equations together eliminates the σ term:
48 + 28 = μ + 2σ + μ - 2σ
76 = 2μ

Dividing both sides by 2 gives us the value of the mean μ:
76/2 = 2μ/2
38 = μ

Therefore, the mean of the test is 38.

I hope this helps! :)