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Solution-HW1_Spr10_ 1

Solution-HW1_Spr10_ 1 - MGMT 305 Homework#1 Page 1 of 4...

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MGMT 305 Homework #1 Page 1 of 4 MGMT 305 Spring 2010 Assignment 1 Solution (Chapters 3, 5, 6) Chapter 3 1. (Total: 12 pts) a. Public Transportation: Automobile: (4 pts) b. Public Transportation: s = 4.64 Automobile: s = 1.83 (6 pts) c. Prefer the automobile. The mean times are the same, but the auto has less variability. (2 pts) Chapter 5 2. a. f (12) = .1144 (1 pt) b. f (16) = .1304 (1 pt) c. P ( x 16) = f (16) + f (17) + f (18) + f (19) + f (20) = .1304 + .0716 + .0278 + .0068 + .0008 = .2374 (4 pts) d. P ( x 15) = 1 - P ( x 16) = 1 - .2374 = .7626 (4 pts) e. E ( x ) = n p = 20(.7) = 14 (2 pts) f. Var ( x ) = n p (1 - p ) = 20 (.7) (.3) = 4.2 (2 pts) σ = = 2.0494 (1 pt) (Total: 15 pts) 3. Binomial n = 10 and p = .09 a. Yes. Since they are selected randomly, p is the same from trial to trial and the trials are independent. (2 pts) b. f (2) = .1714 (2 pts)
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MGMT 305 Homework #1 Page 2 of 4 c. f (0) = .3894 (2 pts) d. 1 - f (0) - f (1) - f (2) = 1 - (.3894 + .3851 + .1714) = .0541 (4 pts) (Total: 10 pts) 4. a. f (12) = Using the binomial tables, f (12) = .1201 (2 pts) b. f (0) + f (1) + f (2) + f (3) + f (4) + f (5) = .0000 + .0000 + .0002 + .0011 + .0046 + .0148 = .0207 (3 pts) c. E ( x ) = np = 20(.5) = 10 (2 pts) d. Var ( x ) = σ 2 = np (1 - p ) = 20(.5)(.5) = 5 (2 pts) σ == 2.24 (1 pt) (Total: 10 pts) Chapter 6 5. (Total: 12 pts) a. .4761 + .1879 = .6640 (4 pts) b. .3888 - .1985 = .1903 (4 pts) c. .4599 - .3508 = .1091 (4 pts) 6. Let x = amount spent μ = 527, σ = 160 a. P ( x > 700) = P ( z > 1.08) = .5000 - .3599 = .1401 (4 pts) b. P ( x < 100) =
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