Question 11A) Cars arrive at Thruway toll booth on an exit ramp on Route 17 in N

Question

Question 11A) Cars arrive at Thruway toll booth on an exit ramp on Route 17 in New York at an average rate of 3.4 cars every five minutes. Assume that the arrival of cars at this toll booth follows the Poisson distribution. A) What is the probability that six or seven cars will arrive at this toll booth during the next five minutes? B) What is the probability that two or more cars will arrive at this toll booth during the next five minutes? C) What is the probability that exactly four cars will arrive at this toll booth during the next 10 minutes?

Explanation / Answer

By poisson distribution,
P(x,m) = e^-m * m^x/x!

Here, m =3.4

a) P(x = 6 or 7) = P(x =6) + P(x =7)
= e^-3.4 * 3.4^6 / 6! +e^-3.4 * 3.4^7 / 7!
= 0.0716 + 0.0348 = 0.1064

b)
P(X >2) = 1 - P(X<=2)
= 1 - e^-3.4 * 3.4^0 / 0! +e^-3.4 * 3.4^1 / 1! + e^-3.4 * 3.4^2/2!
= 1 - 0.0334 + 0.1135 + 0.1929 = 0.6603

c)

Here, m = 3.4/2 = 1.7

P(x = 4) = e^-1.7 * 1.7^4 / 4!
= 0.0636

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