Question

1) 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

c) a score that is 15 points above the mean

d) a score that is 30 points below the mean

e) a score that is 5 points above the mean

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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

c) a z-score of-.1.20

d) a z-score of 1.30

e) a z-score of -0.80

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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

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Answer 1

1)

a)

$z=\frac{x-\mu}{\sigma}=\frac{20}{10}=2.00$

b)

$z=\frac{-10}{10}=-1.00$

c)

$z=\frac{15}{10}=1.50$

d)

$z=\frac{-30}{10}=-3.00$

e)

$z=\frac{5}{10}=0.50$

2)

a)

$x=z\sigma+\mu=1.5\cdot5+43=50.5$

b)

$x=-2\cdot5+43=33$

c)

$x=-1.2\cdot5+43=37$

d)

$x=1.3\cdot5+43=49.5$

e)

$x=-0.8\cdot5+43=39$

3.

a)

$z=\frac{110-150}{5}=-8.00$

b)

$z=\frac{135-150}{5}=-3.00$