Question

5. On a test that has a normal distribution, a score of 48 falls three standard deviations

above the mean, and a score of 24 falls one standard deviation below the mean.
Determine the mean of this test.

Answer 1

The mean is 30

Explanation:

Let's call the mean of the test "μ."

We know that a score of 48 falls three standard deviations above the mean, which can be expressed mathematically as:

48 = μ + 3σ

where σ represents the standard deviation.

Similarly, we know that a score of 24 falls one standard deviation below the mean:

24 = μ - σ

Now we can use these two equations to solve for the mean, μ.

Let's start by isolating σ in the first equation:

48 = μ + 3σ

48 - μ = 3σ

σ = (48 - μ) / 3

We can substitute this expression for σ into the second equation:

24 = μ - σ

24 = μ - [(48 - μ) / 3]

Multiplying both sides by 3 to get rid of the fraction:

72 = 3μ - (48 - μ)

72 = 4μ - 48

120 = 4μ

μ = 30

Therefore, the mean of this test is 30.