The company is opening five new distribution centers within the next year. What
ID: 3043634 • Letter: T
Question
The company is opening five new distribution centers within the next year. What is the probability that fewer than three of the five new centers would be unionized? None of the new centers? Five of the centers?
Distribution Center ID Workers Unionized? (1=For Unionized) Hourly Employee Satisfaction Score Salaried Employee Satisfaction Score Number of Packaging Lines Management Team Average Employment (in years) Accidents per year (Pre-training) Accidents per year (Post-training) 1 0 2 6 8 16 8 4 2 1 2 7 20 5 18 18 3 1 3 6 27 3 18 10 4 1 2 5 2 35 3 1 5 1 3 5 9 1 14 12 6 1 6 7 20 3 15 12 7 1 1 4 27 4 21 20 8 0 2 6 20 3 12 12 9 0 5 6 21 4 19 16 10 0 1 4 9 10 21 15 11 1 1 5 24 7 11 11 12 0 2 4 27 4 4 0 13 0 3 2 19 4 4 2 14 0 2 5 19 10 3 1 15 0 1 4 6 10 14 4 16 1 1 3 15 1 3 3 17 1 1 7 22 7 14 10 18 0 2 5 19 10 3 0 19 0 2 4 20 2 12 9 20 1 2 5 23 20 14 13 21 0 3 5 21 2 12 9 22 0 2 6 14 3 11 11 23 0 1 4 8 3 11 11 24 1 7 4 15 7 16 3 25 0 1 6 16 10 11 5 26 1 1 7 15 30 12 1 27 1 3 5 9 3 6 0 28 0 4 6 13 10 11 6 29 0 7 2 11 4 15 10 30 1 1 7 13 10 11 2 31 1 5 2 19 20 11 3 32 0 7 6 19 5 5 3 33 0 6 3 21 1 14 9 34 0 2 5 18 4 14 1 35 0 7 2 19 2 11 5 36 0 1 4 23 2 13 10 37 0 6 1 24 8 14 6 38 0 2 6 20 15 12 12 39 0 7 3 19 2 11 3 40 0 6 4 26 5 20 10 41 0 1 4 19 4 17 7 42 0 2 6 22 6 17 14 43 0 1 6 26 6 18 10 44 1 2 3 20 27 5 0 45 1 1 7 24 7 12 2 46 0 2 6 26 10 3 1 47 0 2 6 25 7 18 9 48 1 2 7 26 5 17 17 49 1 2 7 23 4 15 14 50 1 2 6 18 2 15 6 51 0 4 7 4 10 3 15 52 0 5 2 12 20 4 0 53 0 1 5 21 42 7 5 54 1 5 6 14 5 12 9 55 0 2 6 8 10 8 1 56 0 3 6 15 5 16 4 57 1 6 7 16 6 21 16 58 0 7 5 19 10 8 2 59 0 3 5 18 4 20 15 60 0 4 5 20 30 13 12 61 1 2 7 20 4 16 18 62 0 2 7 18 4 20 11 63 1 1 6 26 4 13 10 64 0 4 7 18 2 18 12 65 1 2 6 14 3 16 17 66 1 4 5 19 1 17 12 67 1 1 5 20 5 20 18 68 1 4 7 22 12 17 14 69 1 1 7 21 5 5 1 70 0 1 7 18 2 18 12 71 0 4 6 22 4 15 12 72 0 1 7 24 1 17 16 73 0 5 7 24 10 5 0 74 1 6 7 25 8 15 5 75 1 6 1 19 12 12 11 76 1 2 6 19 14 8 5 77 0 5 5 18 1 17 10 78 0 1 7 18 3 18 12 79 1 2 6 21 5 18 18 80 1 2 5 22 5 15 14 81 0 2 5 23 3 18 11 82 0 1 7 19 2 19 10 83 0 1 7 18 14 20 4 84 0 1 7 4 20 7 6 85 0 3 7 12 10 9 5 86 0 4 7 21 5 17 14 87 1 7 3 14 7 14 2 88 1 4 3 8 5 15 10 89 1 5 2 15 9 17 12 90 1 1 5 16 2 13 9 91 0 4 6 15 18 4 1 92 0 1 6 9 18 18 16 93 1 4 5 13 5 14 10 94 1 3 7 11 10 6 5 95 0 2 5 13 2 17 17 96 1 5 3 8 2 19 17 97 1 1 5 14 10 20 19 98 1 2 4 13 2 18 19 99 1 2 6 26 3 20 20 100 0 5 7 24 10 5 0Explanation / Answer
Answer is below:
The probability that the distribution is ionized is .44
This is basically the ratio of ionized by total.
The company is opening five new distribution centers within the next year.
What is the probability that fewer than three of the five new centers would be unionized?
= P(X<3) = P(X=0,1,2) = 5C0 (.44^0)(.56^5) + 5C1 (.44^1)(.56^4)+5C2 (.44^2)(.56^3) = 0.6114
None of the new centers? = P(X=0) =5C0 (.44^0)(.56^5) = 0.0551
Five of the centers? = 5C5 (.44^5)(.56^0) = .0165