Stats for Management

STATISTICS FOR MANAGEMENT

PROBLEMS ON PROBABILITY AND DISTRIBUTIONS

ANSWERS

1. 7/9

2. 0.048

3. 0.2872

4. (a) (0.75)n, (b) 0.288

5. (a) 0.44, (b) 0.404, (c) 0.8982, (d) 0.5556

6. (a) 0.83, (b) 0.086, (c) 0.506, (d) 0.232, (e) 0.08

7. (a) 0.7, (b) 0.3413, (c) (I) 0.692, (II) 0.4878

8. (a) 0.7, (b) 0.25, (c) 0.8673

9. (a) 0.8, (b) 0.7, (c) 0.4286, (d) 0.2143, (e) 0.6

10. (a) 0.3888, (b) 0.2496

11. (a) 0.37, (b) 0.5556, (c) 0.246, (d) 0.214, (e) 0.410, (f) 0.789

12. (a) 0.1, (b) 0.6, (c) 0.3

13. 0.271

14. (a) 0.5, (b) 0.3085, (c) (i) 1.8904, (ii) 0.5217

15. (a) 0.21, (b) 0.8037, (c) 7.82

16. 2.407

17. (a) 0.4, (b) 0.2712

18. (a) 0.3, (b) 5.36

19. 0.1798, 0

20. E(Y – X) = 1, P(Y=3) = 0.375

21. (a) 0.0658, (b) 0.5391, (c) 1.5, (d) 6

22.  k = 0.5, a = 2/3, median = (2/3)+[pic 1], conditional probability = 5/8

23. (a) 2, (b) 0.9647, (c) 0.1856

24. (a) 0.8917, (b) 0.4762, (c) 0.8

25. 0.4667  

26. 1.125

27. (i) 0.48, (ii) 0.4828

28. P(X=0)= 0.336, P(X=1)= 0.452, P(X=2)= 0.188, P(X=3)= 0.024,

       E(X)= 0.9, V(X) = 0.61

29. (a) 0.91, (b) 0.335, (c) 0.78, (d) 0.2271

30. (a) 3/16, (b) 9/16, (c) 3/16, (d) 37/16, (e) 0.7148, (f) 27/16

31. (a) 0.5, (b) 2/3, (c) 2.5, (d) 0.25, (e) 2.3, (f) 7

32. (a) 0.189, (b) 0.095, (c) 1.98, (d) 0.235

33. (a) 0.3278, (b) 0.4891

34. (a) 7/24, (b) 26/9, (c) 77/192, (d) 49/576, (e) 1/2

35. (a) 0.2682, (b) (i) 0.1571, (ii) No, (c) Yes, by Chebycheff’s inequality,

      (d) mean =  – 1.2427, standard deviation = 5.6513

36. (a) 0.7240, (b) 0.4, (c) 0.3125

37. (a) 1.4586, (b) 0.8028, (c) 0.9, (d) 65.667

38. (a) 0.4651, (b) 1/3, (c) 3/64, (d) 12.96, (e) 1.71