Question

1. a normal distribution of scores has a standard deviation of 10. find the z - scores corresponding to each of the following values:

a. a score of 60, where the mean score of the sample data values is 40.
b. a score that is 30 points below the mean, where the mean, where n(40,10).
c. a score of 80, where the mean score of the sample data values is 30.

Explanation:

Step1: Recall z - score formula

$z=\frac{x - \mu}{\sigma}$

Step2: Calculate for part a

$z=\frac{40 - 60}{10}=- 2$

Step3: Calculate for part b

$z=\frac{40 - 10}{10}=3$

Step4: Calculate for part c

$z=\frac{30 - 80}{10}=-5$

Answer:

a. -2
b. 3
c. -5