Answer:
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.