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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.