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
X = 35
X = 70
z = (X – μ) / σ
z = (55 – 50) / 10
z = 5/10 = .5
z = (X – μ) / σ
z = (35 – 50) / 10
z = -15 / 10 = -1.5
z = (X – μ) / σ
z = (70 – 50) / 10
z = 20/10 = 2
X = 40
X = 48
X = 65
z = (X – μ) / σ
z = (40 – 50) / 10
z = -10 / 10 = -1
z = (X – μ) / σ
z = (48 – 50) / 10
z = -2/10 = -.2
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
z = -0.5
z = 1.00
X = μ + zσ
X = 50 + (-2 * 10)
X = 50 + (-20) = 30
X = μ + zσ
X = 50 + (-0.5 * 10)
X = 50 + (-5) = 45
X = μ + zσ
X = 50 + (1 * 10)
X = 50 + 10 = 60
z = 1.5
z = 0.6
z=0
X = μ + zσ
X = 50 + (1.5 * 10)
X = 50 + (15) = 65
X = μ + zσ
X = 50 + (0.6 * 10)
X = 50 + 6 = 56
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
b) μ = 40 and σ = 5
z = (X – μ) / σ
z = (50 – 60) / 5
z = -10/5 = -2
z = (X – μ) / σ
z = (50 – 40) / 5
z = 10/5 = 2
c) μ = 60 and σ = 20
d) μ = 40 and σ = 20
z = (X – μ) / σ
z = (50 – 60) / 20
z = -10/20 = -.5
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.