Suppose a normal distribution has a standard deviation of 15. Judy has a raw score of 120 and a z-score of .5. What is the mean of the distribution?
A) -127.5
B) -112.5
C) +112.5
D) +127.5

Question

Quizplus · Accepted Answer

The formula for converting raw scores to z-scores is:
z = (X - μ) / σ
where X = raw score, μ = mean, and σ = standard deviation

We are given that Judy has a raw score of 120 and a z-score of 0.5. So we can plug in these values and solve for the mean:
0.5 = (120 - μ) / 15
0.5 * 15 = 120 - μ
7.5 = 120 - μ
μ = 120 - 7.5
μ = 112.5

Therefore, the mean of the distribution is 112.5. So the answer is C.

Suppose a Normal Distribution Has a Standard Deviation of 15