Question

scores on the act college entrance exam follow a bell-shaped distribution with mean 18 and standard deviation 6. Wayne's standardized score on the ACT was -0.5. what was Wayne's actual ACT score?

Answer 1

His actual score is 15

Explanation:

Here, we are interested in calculating Wayne’s actual score on the ACT

when we say the scores have being standardized, it means the score was reported in terms of the z-score and not the initial raw scores.

Now, mathematically, for the scores to have a negative z-score, it means it is actually below the mean.

The formula for the z-score or standard score is given below;

z-score = (x - mean)/SD

where in this case, x = ? which is the score we are looking for , z-score = -0.5 , mean score = 18 and standard deviation of the scores = 6

So, substituting these values into the z-score equation, we have;

-0.5 = (x-18)/6

x-18 = 6(-0.5)

x -18 = -3

x = -3 + 18

x = 15