A test has a mean of 153 and a standard deviation of 12, how do you find the test scores that correspond to (a) z= 1.2 and (b) z = -2.4?

1 Answer
Jun 23, 2015

The corresponding scores will be (a) 167.4 and (b) 124.2. Assuming we round to the nearest whole number, this would be 167 and 124 respectively.


Recall that the Z-score of a data point indicates the number of standard deviations that data point is above or below the mean. Thus, a Z-score of 1.2 on data point (a) indicates that (a) is approximately 1.2 standard deviations above the mean of 153, while data point (b) - possessing a Z-score of -2.4 - would lie 2.4 standard deviations below 153.

Thus, the score for (a) is #a = 153 +1.2(12) = 167.4#, and the score for (b) is #b = 153 - 2.4(12) = 124.2#.

Assuming that the test scores must be whole numbers (and thus one cannot gain 0.4 points on a question, for example), we would round these to the nearest whole number, yielding #a = 167, b = 124#.