Question

On a test that has a normal distribution, a score of 16 falls two standard deviations below the mean, and a score of 34 falls one standard deviation above the mean. Determine the mean of this test.

Answer 1

mean = 28

Explanation:

1. A score of 16 is two standard deviations below the mean. If we let μ be the mean and σ be the standard deviation, then this gives us:

μ - 2σ = 16

(1)

2. A score of 34 is one standard deviation above the mean. This gives us:

μ + σ = 34

(2)

Let's solve for μ and σ using these equations.

From (2), we can express σ in terms of μ:

σ = 34 - μ

(3)

Now, plug (3) into (1) to solve for μ:

μ - 2(34 - μ) = 16

Expanding and combining like terms:

μ - 68 + 2μ = 16

3μ = 84

μ = 28