Question #15989

the number of vehicles entering through a university's making gate is 5 in 60 minutes.find the probability that in 90 minutes:(a)no vehicle will enter.(b)at least 2 vehicles will enter.(c)at most 3 vehicles will enter.(d)less than four vehicles will enter.(e)more than 3 vehicles will enter.(f)exactly 5 vehicles will enter

Expert's answer

a) We use a Poissons distribution with a lambda=7.5 (for 90 minutes) and by the formula

P(k=0)=7.5^k/k!*exp(-lambda)=0.0006

b) least two vehicles is 1-P(k=0)-P(k=1) P(k=0) we already know, by the same formula P(k=1)=0.004 and now

P(at least two)=1-0.0006-0.004=0.9954

c) At most three means P(0)+P(1)+P(2)+P(3) by the same formula P(2)=0.016 P(3)=0.039

P(at most 3)=0.059

d) less than four=at most three

e) P(more than 3) = 1-P(at most 3)=1-0.059=0.94

f) P(5)=0.109

P(k=0)=7.5^k/k!*exp(-lambda)=0.0006

b) least two vehicles is 1-P(k=0)-P(k=1) P(k=0) we already know, by the same formula P(k=1)=0.004 and now

P(at least two)=1-0.0006-0.004=0.9954

c) At most three means P(0)+P(1)+P(2)+P(3) by the same formula P(2)=0.016 P(3)=0.039

P(at most 3)=0.059

d) less than four=at most three

e) P(more than 3) = 1-P(at most 3)=1-0.059=0.94

f) P(5)=0.109

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