Contingency Table & Probability

4.55. Problem 2.119 on page 65 describes a survey of 40 MBA students (stored in Grade Survey). For these data, construct contingency tables of gender and graduate major, gender and undergraduate major, gender and employment status, graduate major and undergraduate major and graduate major and employment status.

ID Num Gender Age Height Major Graduate GPA Undergrad Specialization Undergrad GPA GMAT Employment Status Number of Jobs Expected Salary Anticipated Salary in 5 Years Satisfaction Advisement Spending
ID01 M 22 69 IS 3.90 CM 3.30 600 PT 0 45 75 5 200
ID02 M 35 67 A 3.92 O 3.34 480 FT 2 120 250 4 150
ID03 M 31 67 MR 3.77 BU 3.04 550 FT 2 85 120 5 65
ID04 M 28 73 M 3.43 BI 3.41 530 FT 4 100 150 5 150
ID05 M 36 70 EF 3.51 BU 3.12 610 FT 3 80 90 4 300
ID06 F 27 60 A 3.00 SS 3.50 460 FT 3 100 150 4 250
ID07 M 30 68 EF 3.65 CM 3.02 580 FT 5 100 125 4 400
ID08 M 28 66 A 3.00 CM 2.84 590 FT 1 60 100 6 60
ID09 F 24 65 UN 3.22 CM 3.13 570 FT 4 50 60 4 180
ID10 M 33 70 A 3.90 SS 3.24 530 PT 5 50 80 4 700
ID11 M 26 71 A 4.00 BU 3.89 550 FT 3 60 100 5 100
ID12 M 24 74 M 3.20 BU 3.22 500 FT 2 65 100 4 200
ID13 M 31 69 A 3.53 CM 3.33 540 FT 3 80 110 6 300
ID14 M 39 71 EF 3.42 CM 3.04 570 FT 2 100 150 1 100
ID15 F 29 63 MR 3.12 BU 3.14 480 UN 1 50 100 4 1000
ID16 M 26 74 MR 3.43 EN 2.56 600 FT 4 40 65 4 300
ID17 F 23 64 IS 3.75 CM 3.00 580 FT 1 70 100 5 200
ID18 F 26 63 A 3.30 HU 3.23 520 FT 3 60 75 4 150
ID19 M 30 63 EF 4.00 O 3.75 580 FT 3 105 120 6 150
ID20 F 25 63 MR 4.00 BU 3.72 650 FT 1 60 100 4 130
ID21 F 27 62 MR 3.25 ED 3.77 480 UN 2 45 65 4 300
ID22 F 25 63 EF 3.51 BU 3.64 500 FT 2 60 80 4 200
ID23 M 32 73 A 3.35 BU 2.87 580 FT 1 80 140 5 90
ID24 F 31 65 MR 3.22 BU 2.95 540 FT 3 65 85 6 170
ID25 M 25 68 EF 3.47 BU 3.18 590 PT 1 60 150 4 320
ID26 M 29 73 IB 3.67 HU 3.56 620 FT 2 65 135 4 200
ID27 F 25 64 MR 3.40 SS 3.26 600 FT 2 55 90 4 600
ID28 M 37 68 M 3.65 EN 3.41 530 FT 2 90 130 2 200
ID29 M 34 66 A 3.54 BI 3.38 540 FT 1 70 100 3 100
ID30 F 33 61 M 3.64 ED 2.79 570 FT 2 45 80 4 160
ID31 F 38 65 EF 4.00 BU 3.78 570 PT 1 80 110 4 230
ID32 M 30 72 EF 3.70 PS 3.55 550 FT 2 75 150 5 500
ID33 M 32 73 M 3.24 PA 3.17 580 FT 2 60 85 6 250
ID34 F 28 61 A 3.37 SS 3.68 610 FT 1 75 95 3 150
ID35 F 27 66 IS 3.56 CM 3.27 560 FT 1 65 90 4 120
ID36 M 41 74 IB 3.28 SS 3.65 490 FT 1 50 85 1 160
ID37 F 35 65 M 3.16 PS 3.29 510 FT 3 75 100 2 100
ID38 F 25 63 IS 3.59 CM 3.45 560 FT 1 60 90 3 160
ID39 M 32 70 EF 3.80 EN 3.03 600 FT 2 90 160 7 130
ID40 M 30 69 M 3.15 O 3.22 540 PT 1 55 85 6 110

a. For each of these contingency tables, compute all the conditional and marginal probabilities.

b. Based on (b), what conclusions can you reach about whether these variables are independent?

5.24. Investment advisors agree that near-retirees, defined as people aged 55 to 65, should have balanced portfolios. Most advisors suggest that the near-retirees have no more than 50% of their investments in stocks. However, during the huge decline in the stock market in 2008, 22% of near-retirees had 90% or more of their investments in stocks (P. Regnier, "What I Learned from the Crash," Money, May 2009, p. 114). Suppose you have a random sample of 10 people who would have been labelled as near-retirees in 2008.

What is the probability that during 2008

a. Zero had 90% or more of their investment in stocks?

b. Exactly one had 90% or more of his or her investment in stocks?

c. Two or fewer had 90% or more of their investment in stocks?

d. Three or more had 90% or more of their investment in stocks?

5.31. Assume that the number of network errors experienced in a day on a local area network (LAN) is distributed as a Poisson random variable. The mean number of network errors experienced in a day is 2.4. What is the probability that in any given day

a. Zero network errors will occur?

b. Exactly one network error will occur?

c. Two or more network errors will occur?

d. Fewer than three network errors will occur?