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Practice Questions 4 Answers 1. a. C b .B c. D d. A 2. a. C b. D c. B 3. a. B b. C 4. a. A b. D 5. a. D b. C 6. a. B b. A 7. a. D b. B c. C d. B e. A f. D g. A h. B i. C 8. a. D b. A 9. a. C b. A 10. B 11. B 12. D 13. A 14. C 15. D 16. A 17. C 18. B 19. a. P ( X > 8) = (20-8) / (20-0) = 12 / 20 = 0.60 b. P (10 < X < 15) = (15-10) / (20-0) = 5 / 20 = 0.25 c. The range is a total of 20 minutes. Seventy percent of the time, you should be called in before you wait 14 minutes. 20.

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a. 0.3859 b. 0.8907 c. 0.6985 d. 0.5549 21. a. k = -0.95 b. k = 0.18 c. k = 1.04 d. k = 1.33 22. P = 0.24, n = 50, μ = E ( X ) = nP = 12, 2 σ = Var( X ) = nP (1-P) = 9.12, σ = 3.02 Without continuity correction P ( X >10) = P ( Z >-0.66) = 0.7454. 23. a. E ( T ) =1/ λ =15.2, then, λ = 0.0658, and P ( T > 45) = 45 2.961 e e λ - - = = 0.0518 b . P ( T < t ) = 0.90, 1- t e λ - = 0.90 > 0.0658 t e - = 0.10 > -0.0658 t =-2.3026 > t ; 35 minutes 24. a. 18 to 30 minutes represent 80% of the distance between 15 and 30 minutes. Hence, P ( X >18) = 0.80. b. 21 to 27 minutes represents 40% of the distance between 15 and 30 minutes. Hence, P (21 > X X 27) = 0.40. c. X μ = 4.1 and 2 X σ = 1.69. Labor cost per minute = \$0.10, Y = 0.10 X . Y μ = 0.10 X μ = (0.10)(4.1) = \$0.41, 2 Y σ = ( 29 2 2 0.10 X σ = 0.0169. Hence, Y σ = 0.113. 25. P ( X > k ) = 0.10 > P [ Z > ( k -287) / 15] = 0.10 > ( k -287) / 15 = 1.28 > k = \$306.20 26. P ( X > k ) = 0.05 > P [ Z > ( k -84) / 4] = 0.05 > ( k -84) / 4 = 1.645 > k = 90.58 ; 91 meals 27. P = 0.621, n = 150, μ = E( X) = 93.15, 2 σ =Var( X ) = nP (1- P ) = 35.3039, σ X = 5.942 P ( X > 80) = P ( Z > -2.21) = 0.9864.
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