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C291MT2013_Solutions

D 2 138 need all three parts for the 2 marks no part

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d) [2 marks] 15, 189, 138 (Need all three parts for the 2 marks; no part marks here) e)[1 mark] E. Monthly sales are more variable in Vancouver compare to Toronto Question 4 (10 marks) a) (i) [1 mark] A. Negative, moderately strong (ii) [1 mark] B. Become stronger negative b) [3 marks] Large neg.; Large Pos.; Small c) [5 marks] False, False, False, False, True Q uestion 5 (12 marks) a) [2 marks] = 74.73 – 3.19 x (Reason: = 59.5 –(-3.19)(5.4) = 74.73) b) [2 marks] -0.95 (Reason: Rearrange the formula for = (-3.19)(3.3/11.1) = -0.95) c) [1 mark] “ decreases by 3.19 d) [1 mark] 90% (Reason: r 2 = (-0.95) 2 = 0.90 or 90% e) [1 mark] 49 (Reason: (8) = 74.73 – 3.19(8) = 49.21) f) [2 marks] Residual = 11 (Reason: y– = 60 – 49 =11) Yes, this is an outlier since the resident is more than 2.5 ’s away from 0. g) [1 mark] 57.5 (Reason: Since x is unknown, just use the mean of y .) h) [2 marks] 35 to 80 (Reason: Use the 68-95-99.7 Rule, i.e. 57.5±2(11.1) = 35.3, 74.7) 1
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Question 6 (18 marks) a) [2 marks] A. I and II only b) (i) [2 marks] Mean = 20 ; SD = 10 Computations: Pr(Z > z) = 0.5 => z = 0, so X = μ + zσ => 20 = μ + 0 => μ = 20 Pr(Z > z) = 0.1587 => z = 1, so X = μ + zσ => 30 = 20 + 1σ => σ = 10 (ii) [2 marks] A. Computations: Pr(15 < X < 25) = Pr([15-20]/10 < Z < [25-20]/10) = Pr(-0.5 < Z < 0.5) = 1 – 2(0.3085) = 0.383 c) (i) [2 marks] Mean = 95 ; SD = 5 Computations: E(X+Y) = E(X) + E(Y) =15 + 80 = 95; Var(X+Y) = Var(X) + Var(Y) (since indep.) = 10 + 15 = 25, so SD =√25 = 5 (ii) [2 marks] Mean = 2375 ; SD = 25 Computations: E(T) = 25(95); Var(T) = 25(25) = 625; SD = √625 = 25 d) (i)[2 marks] A. 0.4 minutes (Reason: σ/√n = 2/√25 = 0.4)
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