Question

The results of a common standardized test used in psychology research are designed so that the population mean is 115, and the standard deviation is 20. A subject earns a score of 89.

What is the z-score?

Answer 1

A z-score is calculated by subtracting the mean from the raw score and then dividing by the standard deviation. For a score of 89 with a mean of 115 and a standard deviation of 20, the z-score would be -1.3, indicating the score is 1.3 standard deviations below the mean.

Step-by-step explanation:

To calculate the z-score for a standardized test score, we use the formula:

z = (x - μ) / σ

Where x is the raw score, μ is the population mean, and σ is the standard deviation. In this case, the student earned a score of 89, the population mean (μ) is 115, and the standard deviation (σ) is 20.

Substitute the given values into the formula:

z = (89 - 115) / 20

z = -26 / 20

z = -1.3

This means the subject's score of 89 is 1.3 standard deviations below the mean on this standardized test.