Quantitative Literacy Practice Exam

If scores on a test have a mean of 75 and a standard deviation of 9, what is Anna's z-score if she scores 78?

1. 0.5

2. 0.33

3. 1.0

4. 1.5

The correct answer is: 0.33

To find Anna's z-score, you need to understand that the z-score is a measure of how many standard deviations an individual score is from the mean of the data set. The formula for calculating a z-score is given by: \[ z = \frac{(X - \mu)}{\sigma} \] where: - \( X \) is the individual score, - \( \mu \) is the mean score, - \( \sigma \) is the standard deviation. In this case, Anna’s score is 78, the mean is 75, and the standard deviation is 9. Plugging these values into the formula: 1. Subtract the mean from Anna's score: \( 78 - 75 = 3 \) 2. Divide this result by the standard deviation: \( \frac{3}{9} = 0.33 \) Therefore, Anna's z-score is 0.33, reflecting that her score is approximately one-third of a standard deviation above the mean. This correctly indicates her relative position within the distribution of scores. This is why the z-score of 0.33 is the correct answer, as it accurately represents Anna's performance in relation to the mean.