On a nationwide math test, the mean was 72 and the standard deviation was 10. If Roberto scored 75, what was his z-score? Round your answer to the nearest hundredth.

Answer 1

Remember that a z-score is the number of standard deviations the score in question is above the mean (for positive z-scores) or below the mean (for negative z-scores).

In this example, the test score in question (75) is 3 points higher than the mean score of 72 which is shown in the denominator of William's equation that I copied below for your reference.

That 3 point difference between the test score of 75 and the mean of 72 is then divided by the standard deviation (10) to get our test score's number of standard deviations above or below the mean (a z-score of +.3 in this case).

The score of 75 is therefore .3 standard deviations above the mean. A z-score of +.3.

Equation provided by William W:

z_score =(actual - mean)/(standard deviation)

z_score = (75 - 72)/10 = +3/10 = .3

Answer 2

Use the equation:

z_score =(actual - mean)/(standard deviation)

z_score = (75 - 72)/10