Question

The AAT (a standardized test) is normally distributed with a mean of 200 and a standard deviation of 50. Calculate the z-score for a score of 180 and interpret its meaning.

Answer 1

The z-score for an AAT score of 180 is -0.4, indicating that the score is 0.4 standard deviations below the mean test score.

Step-by-step explanation:

The question asks to calculate the z-score for a score of 180 on an AAT test, which has a mean score (μ) of 200 and a standard deviation (σ) of 50. The z-score formula is z = (x - μ) ÷ σ, where x is the score. Plugging the values into the formula gives us z = (180 - 200) ÷ 50 = -20 ÷ 50 = -0.4. This z-score indicates that a score of 180 is 0.4 standard deviations below the mean score of 200 for the AAT test.