Open-ended1. Tree - DiagramFirst BranchesP(Bus) = .65P(Run) = .35Next Four BranchesP(Late | Bus) = .25P(On Time | Bus) = .75P(Late | Run ) = .95P(On Time | Run) = 0.05Multiply Across Each BranchP(Late and Bus) = 0.1625P(On Time and Bus) = 0.4875P(Late and Run ) = 0.3325P(On Time and Run) = 0.0175a.P(Run | On Time) = P(Run and On Time) / P(On Time) = 0.0175 / (0.0175 = 0.4875) = 0.0346b.P(Late | Bus) is directly on the tree. Simply equals 0.25.___________________________________________________________2. This is binomial with fixed trials n=6, p = 0.25a. (6 choose 3) .25^3 .75^3 = .1318 for the ? mark underneath 3(6 choose 6) .25^6 .75^0 = 0.0002b. P(4 or more) = P(4) + P(5) + P(6)0.0330 + 0.0044 + 0.0002 = 0.0376c. Use Bayes RuleP(X = 1 | X < 2) = P(X = 1 and X < 2) / P(X < 2) = .3560 / (.3560 + .1780) = 0.66666d. Normal Approximation to Binomial (or CLT)n = 115p = 1/5 = 0.2mu = 115 x 0.2 = 23sigma = sqrt(115 x 0.2 x 0.8) = 4.2895Now find a z-scorez = (30 - 23)/4.2895 = 1.63Look up 1.63 on z-table to get .9484We need 30 or more so do 1 - .9484 = 0.0516___________________________________________________________V1cccbaacabe(no actual question)aacV2bccce(no actual
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