Math 115a Answer Key to Study Guide for the Final _071 1. a) i) region 1 and 4 ii) region 3 iii) region 2 b) i) 0.55 ii) 0.3 iii) 0.15 iv) 0.85 v) 0.35 vi) 0.35 vii) 0.6 viii) 2/3 c) i) not B or not F; ()()CPB F∩ or ()CCPB F∪ d) Not independent and not mutually exclusive e) Not independent but they are mutually exclusive 2. a) 70% b) 48% c) 6% d)24% e) 82% f) 94% g) 20% h) 25% 3. (B) 4. 53.51%≅ b) 87.48%≅ c) 77.78%≅ 5. (C) 6. (C) 7. 40 8. (B) 9.()159522jj=−∑ 10. (C) 11. (D) 12. a) Sample space is {7, 12, 25, 30} (7).25PX== ( 12) .25PX== (25).25PX== ( 30) .25PX== b) (25).25PX== c) ( 15) ( 12) 0.5PX PX<=≤= d) ( ) $18.50EX= e) If repeated many, many times, the average amount per draw would be $18.50 13. Stock A The expect value of Stock A is $59 and the expect value of Stock B is $14 14. a) $17 b) $30 15. (B) 16. (B) 17. a) b) c) 8 night games with pizza and soda quantities were at least 400 d) 385.5 is the average quantity of sodas at day games 18. (C) 19. (D) 20. a) 0.1345 b) ≅ 0.0223 .35 .15 .3 .2 123421. a) b) 130.481527≅ c) 140.518527≅ d) Option B 22. A is an Accident and D is Driver training Course a) ( ) 0.18PA= b) 1(|)3PD A= 23. a) 80% b) 51.61%≅ 24. (D) 25. (D) 26. a) 0.5 b) 0.4 c) 0.5 d) 1/16 27. a) b) 28. a) $108,805.30 b) $117,894.86 c) $117,939.31 29. a) $1639.49 b) 5.09% c) $1637.46 d) 5.127% 30. a) 2.52% b) 2.503% 31. a) 15.6959 years b) 15.6944 years 32. (C) 33. a) 8.327% b) 8.158% 34. 701,565 people 35. a) continuous b) finite c) finite 36. False 37. a) 0.091 b) .3799 c) 00.1225 0 1.3799 1 2().6599 2 3.8494 3 4.9404 4 515XxxxFxxxxx<≤<≤<=≤<≤<≤<≥ d) 2.0479 Bin Frequency18 4 20 3 22 1 24 2 More 038. b) .00045 4 out of 5 garments are returned c) .5 39. a) Area under the curve must equal 1: ()() ()1111 1 122 += b) ( 100) 0.5Py>= Area under the curve c) ( 100) 0.5Py<= Area under the curve d) ( 100) 0Py== 40. (D) 41. a) ()10 6006000Xxfxelsewhere≤≤= ()0010 6006001 600XxFx x xx<=≤≤> b) 1( 200)3PX≤= c) 300 feet from the start d) 1(300 500)3Px≤≤ = 42. (C) 43. a) ( 36) 0.4066PL≥= b) ( 36) 0PL== c) .0137 height of the graph d) .4512 45.12% that the lifetime of a light bulb will last at most 24 months e) 55.45 months 44. (A) 45. a) p.m.f. b) p.d.f. c) p.m.f. d) none e) c.d.f. of a finite rv f) p.d.f. 46. a) p.m.f. since T takes on values 0, 1, 2, 3, 4 where 0 represents those you don’t have regular brands b) 0.85 c) 0.5 d) 1.65 47. a) (3 15) 0.8Pt<≤ = b) ( 12) 0.25Pt>= 48. (D) 49. (E) 50. a) 0.03 b) 0.62 c) 1 d) no (6.29 > 5) e)
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