Question

Problem 1 You're a systems engineer working for a consulting company that works on short-term engineering projects. The distribution of the lengths of the 48 projects undertaken by the company in 2018 are shown in the table below. Use the event notation A chosen project had length i Graphically depict the lengths of the projects from 2018. Enumerate the probabilities of P(A) for all i Find the probability that a randomly chosen project took longer than three weeks. You randomly chose to examine two projects. What is the probability that you chose projects of length two weeks and four weeks? You randomly chose to examine two projects. Find the probability that at least one of the projects took longer than three weeks. a. b. c. d. e. Project length Count 1 10 15 12 4

Answer 1

Project Length (Weeks)	Number of Projects	Cumulative Frequency
1	3	3
2	10	13
3	15	28
4	12	40
5	8	48

(a)

(b)
Project Length (Weeks)	Number of Projects	Probability
1	3	0.063
2	10	0.208
3	15	0.313
4	12	0.250
5	8	0.167
(c) P(Longer than 3 weeks) = 0.250 + 0.167 = 0.417
(d) Probability = C[(10 + 12), 2] / C(48, 2) = C(22, 2)/C(48, 2) = 0.205
(e) P(At least one project took longer than 3 weeks) = 1 - P(Neither project took longer than 3 weeks) = 1 - [{C(3 + 10 + 15), 2)}/C(48, 2)] = 1 - {C(28, 2)/C(48, 2)} = 0.665