Question

The results of a common standardized test used in psychology research is designed so that the population mean is 175 and the standard deviation is 30. A subject earns a score of 166. What is the z-score for this raw score?

Answer 1

The z-score for a raw score of 166, with a mean of 175 and a standard deviation of 30, is -0.3. This indicates that the score is 0.3 standard deviations below the mean.

Step-by-step explanation:

To calculate the z-score for a raw score of 166, when the population mean is 175 and the standard deviation is 30, we use the formula z = (X - μ) / σ, where X is the raw score, μ is the mean, and σ is the standard deviation.

Using the provided values, the calculation is as follows:

z = (166 - 175) / 30
z = -9 / 30
z = -0.3

Therefore, the z-score for a raw score of 166 is -0.3. This means that the score is 0.3 standard deviations below the mean.