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# ismch05 - 58 Instructors Solutions Manual for Statistics...

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58       Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition Chapter 5: Discrete Random Variables and Probability Distributions 5.1 a. Discrete b. Discrete c. Discrete d. Discrete 5-2 Discrete 5-3 Various answers including; the number of business phone calls on the first day of business, the number of customers in the first month, the number of employees hired in the first week, the number of proposals produced for new clients. 5-4 Total sales, advertising expenditures, competitor’s sales 5-5 Various answers X –# of times missing class P(x) F(x) 0 .65 .65 1 .15 .80 2 .10 .90 3 .09 .99 4 .01 1.00 5-6 a. P(3 ≤ x <) = .20 + .20 + .15 = 0.55 b. P(x > 3) = .20 + .15 + .10 = 0.45 c. P(x ≤ 4) = .05 + .10 + .20+ .20 + .20 = 0.75 d. P(2 < x ≤ 5) = .20 + .20 + .15 = 0.55 5-7 a. Cumulative probability function: X 0 1 2 3 4 5 6 7 8 9 P(x) .10 .08 .07 .15 .12 .08 .10 .12 .08 .10 F(x) .10 .18 .25 .40 .52 .60 .70 .82 .90 1.00 b. P(x ≥ 5) = .08 + .10 + .12 + .08 + .10 = .48 c. P(3 ≤ x ≤ 7) = .15 + .12 + .08 + .10 + .12 = .57

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59       Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition 5-8 a. Probability function: 4 3 2 1 0 0.4 0.3 0.2 0.1 0.0 Number of Returns Probability: P(x) Probability distribution function Proportion of new cars returned: Correction of defects b. Cumulative probability function: 0 1 2 3 4 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Number of Returns Cumulative probability: F(x) Cumulative probability function Proportion of new cars returned: Correction of defects c. μ = 0 + .36 + 2(.23) + 3(.09) + 4(.04) = 1.25 defects d. 2 2 ( ) x Px x σ = = 1.1675 defects
Chapter 5: Discrete Random Variables and Probability Distributions        60 e. Excel output: 5.9 a. Probability function: 5 4 3 2 1 0 0.3 0.2 0.1 Orders Probability: P(x) Probability distribution function New furnace orders resulting from pre-winter service calls

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61       Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition b. Cumulative probability function: 0 1 2 3 4 5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Orders Cumulative probability: F(x) Cumulative probability function New furnace orders resulting from pre-winter service calls c. P(x ≥ 3) = .50 d. μ = 2.45 orders e. σ = 1.3592 orders f. Excel output:
Chapter 5: Discrete Random Variables and Probability Distributions        62 5.10 a. Probability function 53 52 51 50 49 48 47 0.3 0.2 0.1 0.0 Clips Probability: P(x) Probability distribution function Number of paper clips per package b. Cumulative probability function 53 52 51 50 49 48 47 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Clips Cumulative probability: F(x) Cumulative probability function Number of paper clips per package c. P(49 x 51) = .70 d. 1 – [P(x < 50)] 2 = 1 – .1444 = .8556 e. μ = 47(.04) + 48(.13) + 49(.21) + 50(.29) + 51(.20) + 52(.10) + 53(.03) = 49.9 clips 2 σ = 1.95 clips σ = 1.3964 clips

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63       Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition Excel output: f. Mean and standard deviation of profit per package: π = 1.5 – (.16 + .02X) μ = E( π ) = 1.5 – (.16 + (.02)(49.9)) = \$.342 π σ = |.02|(1.3964) = \$.0279
Chapter 5: Discrete Random Variables and Probability Distributions        64 5.11 a. Probability function 7 6 5 4 3 2 1 0 0.3 0.2 0.1 0.0 Riders Probability: P(x) Probability distribution function Number of bus riders b. Cumulative probability function: 7 6 5 4 3 2 1 0 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Riders Cumulative probability: F(x)

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ismch05 - 58 Instructors Solutions Manual for Statistics...

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