Question

Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time period, is characterized by the following discrete probability function: f(x) = e −6 6x x! , for x = 0, 1, 2, . . . .

(a) Find the probability that in a specific 20-second time period, more than 8 cars arrive at the intersection.
(b) Find the probability that only 2 cars arrive

Answer 1

a) P(x>8) = 0.3937

b) P(x = 2) =0.04661

Explanation:

a) From to find the probabilty that in this specific time period, more than 8 cars arrive at the intesection, we use the probability function thus

P(x>8) = 1 - P(x≤8), Cause you can use the complement for calculate this probability , then:

P(x≤8) =
`(e^(-6)*6^(0) )/(0!)+(e^(-6)*6^(1) )/(1!)+(e^(-6)*6^(2) )/(2!)+...` , until x= 8, then you obtain:

P(x≤8)=0.6063 and

P(x>8) = 1 - P(x≤8)= 1-0.6063 = 0.3937

b) P(x=2)=
`(e^(-6)*6^(2)  )/(2!)`

P(x = 2) =0.04661