Question

A traffic control engineer reports that 60% of the vehicles passing through a checkpoint are from within the state. What is the probability that fewer than 2 of the next 9 vehicles are from out of state? Use the Binomial table from the back of the book

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Answer 1

00 100 solution : 7 given that, A trafic control engineer reeports that 60% of the vehicles passing through a Checkpoint are from within the state. e percentage of vehicles out of State - 100 -60 = 40% -> We take Success as vehicles from out of state. i probability of success þ = 40% => p = 40 => p=0,4 Total number of vehicles n=9. Take random Variable x as number of vehicles are from out of state. so we have to find probability that fewer than 2 of the next g vehicles are ºfH00 out of State. & we find P (X<2). We use binomial formula as below. (?) = ! P(X=x) = (2) Þ{(1-5)- X!(n-021 oo P(x+2) = P(x=0) + P(x = 1) (%) (04) (1-0.4)"° + (9) (0.4)' (1-0.4)91 9! XIX (0.6) 9. (014) (0.6) 0!(9-0) ! (9-)! q! *(0,6)' + + 9x81 9! Ex(0.4)(0.6) 뒝 = 0.01008 + 0,06047 = 0,07055 in parobability of fewer than a of the next g Vehicles are from out of State = 0.07055, n-2 9-0 - 8 + 8 -X

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