Answers to Homework Assignment #1



Answers to Homework Assignment #1 – Psychology 331

Chapter 5:

6) A population has a mean of μ = 50 and a standard deviation of σ = 10.

a) For this population, find the z-scores corresponding to each of the following:

X = 55

z = (X – μ) / σ

z = (55 – 50) / 10

z = 5/10 = .5

X = 40

z = (X – μ) / σ

z = (40 – 50) / 10

z = -10 / 10 = -1

X = 35

z = (X – μ) / σ

z = (35 – 50) / 10

z = -15 / 10 = -1.5

X = 48

z = (X – μ) / σ

z = (48 – 50) / 10

z = -2/10 = -.2

X = 70

z = (X – μ) / σ

z = (70 – 50) / 10

z = 20/10 = 2

X = 65

z = (X – μ) / σ

z = (65 – 50) / 10

z = 15/10 = 1.5

b) For the same population, find the score (X value) corresponding to each of the following scores:

z = -2.00

X = μ + zσ

X = 50 + (-2 * 10)

X = 50 + (-20) = 30

z = 1.5

X = μ + zσ

X = 50 + (1.5 * 10)

X = 50 + (15) = 65

z = -0.5

X = μ + zσ

X = 50 + (-0.5 * 10)

X = 50 + (-5) = 45

z = 0.6

X = μ + zσ

X = 50 + (0.6 * 10)

X = 50 + 6 = 56

z = 1.00

X = μ + zσ

X = 50 + (1 * 10)

X = 50 + 10 = 60

z = 0

X = μ + zσ

X = 50 + (0 * 10)

X = 50 + 0 = 50

10) Find the z-score corresponding to a score of X = 50 for each of the following distributions.

a) μ = 60 and σ = 5

z = (X – μ) / σ

z = (50 – 60) / 5

z = -10/5 = -2

b) μ = 40 and σ = 5

z = (X – μ) / σ

z = (50 – 40) / 5

z = 10/5 = 2

c) μ = 60 and σ = 20

z = (X – μ) / σ

z = (50 – 60) / 20

z = -10/20 = -.5

d) μ = 40 and σ = 20

z = (X – μ) / σ

z = (50 – 40) / 20

z = 10/20 = .5

20) For each of the following populations, would a score of X = 48 be considered a central score (near the middle of the distribution) or an extreme score (far out in the tail of the distribution)?

a) μ = 40 and σ = 10

X = 48 would be between the mean and 1 SD above the mean, so it is a central score.

b) μ = 40 and σ = 2

X = 48 would be 4 SDs above the mean, so it is an extreme score.

c) μ = 50 and σ = 4

X = 48 would be between the mean and one SD below the mean, so it is a central score.

d) μ = 60 and σ = 4

X = 48 would be 3 SDs below the mean, so it is an extreme score.

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