Question

A researcher has compiled a set of scores witha mean of u=39 and a standard deviation of 4 WHat is the z-score for the raw score X=28?

a. z=-.50
b. z=+2.75
c. z=-2.75
d. z=+.60

Answer 1

The z-score for a raw score of 28, with a mean of 39 and standard deviation of 4, is calculated as -2.75, placing the score 2.75 standard deviations below the mean.

Step-by-step explanation:

To calculate the z-score for a raw score of X=28 when the mean (u) is 39 and the standard deviation is 4, use the z-score formula:

Z = (X - μ) / σ

So, substituting the given values we get:

Z = (28 - 39) / 4

Z = -11 / 4

Z = -2.75

Therefore, the z-score that corresponds to the raw score of 28 is -2.75, which means this score is 2.75 standard deviations to the left of the mean.

The correct answer from the provided options is: c. z=-2.75.