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

Answer:

0.2905

Step-by-step 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 ) = $\frac{70^k e^{-70} }{k!}$

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

=$1-\Sigma_{i=1}^{i=74} e^{-70} (\frac{\lambda ^i}{i!} )$

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