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# Answers to Homework 5 - Answers to Homework 5 Pg 160-162 23...

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Answers to Homework 5 Pg. 160-162: 23, 24, 26 & 28 Pg. 195-197: 2, 5(a,d), 6(b, c), 7(a,c), 8(b,d), 10(a,c), 11(b, c, d), 12a, 14(a, b, c), 15a, 16a, 18a, 19(a,b) & 21(a, b, c) 23. a) Z = X μ 43-40 = 3/2 = 1.5 OR b) 60-50 = 10/20 = 0.5 σ 2 20 I would expect a better grade on the exam with a 43 because when the score is standardized a score of 1.5 is higher than a score of .50. I would rather be one and half standard deviations above the mean than only a half of a standard deviation. 24. a) Z = X μ 55-60 = -5/5 = -1 OR b) 40-50 = -10/20 = -0.5 σ 5 20 I would expect a better grade on the exam with a 40 because I would rather be a half standard deviation below the mean than a full standard deviation below the mean. 26. a) Z = X μ 48-38 = 10/20 = 0.5 σ 20 (Z*   σ ) +  µ   =   (0.5*10) + 50 = 5 +50 =  55 b) Z = X μ 40-38 = 2/20 = 0.1 σ 20 (Z* σ ) + µ = X (0.1*10) + 50 = 1 +50 = 51 c) Z = X μ 30-38 = -8/20 = -0.4 σ 20 (Z* σ ) + µ = X (-0.4*10) + 50 = -4 +50 = 46 d) Z = X μ 18-38 = -20/20 = -1 σ 20 (Z* σ ) + µ = X (-1*10) + 50 = -10 + 50 = 40 28. a) µ = 0+6+4+3+12/5 = 25/5 = 5 X X-M (X-M) 2 0 -5 25 6 1 1 4 -1 1 3 -2 4

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12 7 49 0 80 SS / (N) = variance √variance = SD 80/(5) = 16
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