Question

Vehicle arrivals at a certain intersection from 9-10 am have a Poisson distribution = 70/hr. A Berkeley TE student counts arrivals at the intersection during this time period for a number of days. 1. Write an exact expression for the probability that 75 or more vehicles will be counted on a particular day

Answer 1

0.2905

Explanation:

Given that vehicle arrivals at a certain intersection from 9-10 am have a Poisson distribution = 70/hr.

Also given that A Berkeley TE student counts arrivals at the intersection during this time period for a number of days.

To find the probability for 75 or more vehicles

Let X be the no of vehicles

P(k events ) =
`(70^k e^(-70) )/(k!)`

Hence here required probability=
`P(X\geq 75)`

=
`1-\Sigma_(i=1)^(i=74)  e^(-70) ((\lambda ^i)/(i!) )`

Reqd prob =
`P(X\geq 75)=0.29048`