advertisement

c Math 166 WIR, Spring 2011, Benjamin Aurispa Math 166 Final Exam Review Answer Key 1. (a) Regular (b) Absorbing (c) Neither 2. (a) 4 months later, 44.07% will buy Coke, 31.14% will buy Pepsi, and 24.79% will buy Dr. Pepper (b) 0.1874 127/281 (c) X = 91/281 63/281 1 0 3/7 29/49 0 1 4/7 20/49 3. L = 0 0 0 0 0 0 0 0 In the long run, if you start in state C, the probabilities are 73 and 74 that you will eventually be 20 absorbed by states A and B respectively. If you start in state D, the probabilities are 29 49 and 49 that you will eventually be absorbed by states A and B respectively. 3 32 7 4. 11 t − 11 , 11 t + 17 , t , where t is any real number. 11 5. a = 26, b = −13, c = 4, d = 9 6. (a) $1140.41 (b) $165,123 (c) $255.41 (d) $58,988.35 7. 250,000 8. a = 25, b = 31, c = 45, d = 11, e = 73, f = 42, g = 30, h = 43 (a) 160 (b) 145 (c) 9. 84 300 = 7 25 13 60 10. (a) (b) (c) (d) 29 35 29 35 ; 29 to 4 1 20 = 5 8 4 22 = 11 6 (e) Not mutually exclusive since E and F CAN occur at the same time. (f) Yes, they ARE independent since P (E ∩ F ) = P (E) · P (F ). 11. (a) 6,012,580 (b) 0.8777 1 c Math 166 WIR, Spring 2011, Benjamin Aurispa 12. (a) 693 5512 ≈ 0.1257 (b) They are NOT independent since P (D ∩ F ) 6= P (D) · P (F ). 13. −$0.28 14. 0.0033 15. (a) 2,592,000 X Prob (b) 0 1 2 11 24 11 24 1 12 16. (a) 5 years (b) $5135.96 (c) $51.79 17. (a) E = {1A, 1Ac , 2A, 2Ac , 3A, 3Ac , 4A, 4Ac } (b) No, not all outcomes are equally likely (c) E = {1A, 2A, 3A, 3Ac , 4A} (d) 6 13 18. (a) 0.2023 (b) 12,844.0386 pounds 19. (a) {2, 4} (b) {1, 2, 3, 4, 6} (c) False (d) False (e) True 20. Regions a, b, c, f, and h are shaded 21. 360,360 22. (a) X = Number of Cheetos (b) Mean = 105.1765, Median = 100, Mode= 95, σ = 9.0569, V ar(X) = σ 2 = 82.0277 23. (a) The Aggies are going to the Cotton Bowl and beat Oklahoma, or they did not beat Missouri. (b) (r∧ ∼ p) Y (q ∧ ∼ p) (c) See Full Solutions 24. (a) X = 1, 2, 3, 4, . . .; X is Infinite Discrete (b) X = 0, 1, 2, . . . , 12; X is Finite Discrete (c) X = 1, 2, 3, . . . , 40; X is Finite Discrete 25. 2 goldfish, 48 tetras, 24 guppies 26. 9.5% 27. (a) 0.1106 (b) 6 2 c Math 166 WIR, Spring 2011, Benjamin Aurispa 28. $5971.46; Interest is $1028.54 29. (a) 2 × 2 (b) Not Possible (c) Not Possible 30. 4,968,000 3