Question

A normal distribution of scores has a variance of S squared = 100. Find the z-scores corresponding to each of the following values:

a) a score that is 20 points above the mean

b) a score that is 10 points below the mean

2) Given a mean score of 43 and a standard deviation of 5 for teaching readiness test among a sample of students calculate raw scores for the following:

a) a z-score of 1.50

b) a z-score of -2.00

3) Subjective wellbeing was measured among a sample of Statistics students with M=150 and S squared=25. Determine the z-scores for the students who obtained the following scores on the subjective wellbeing measure.

a) 110

b) 135

Answer 1

1. $\sigma = \sqrt{100}=10$

a) $Z = \frac{20}{10} = 2$

b) $Z = \frac{-10}{10}=-1$

2. $\mu=43$

$\sigma = 5$

a) $1.5 = \frac{x-43}{5}$

7.5 = x-43

x=50.5

b) $-2.0=\frac{x-43}{5}$

-10=x- 43

x=33

3. $\mu=150$

$s^2=25$

s=5

a) $Z = \frac{110-150}{5}=-8$

b) Z $= \frac{135-150}{5}=-3$