Question

The number of cars passing through the M50 toll follows a Poisson distribution with a rate of lambda = 90000 cars per day. What is the probability that more than 187950 euro is collected in tolls on a given day? (correct to 4 decimal places)

Answer 1

events/time = 90,000 cars/day

Plk events in time period) = eerients time period. (time * time period)" k!

according to the formula P(187950 in 1 day) :

since the price of the toll is not given, we cannot calculate no. of cars for collecting 187950 euros,

let us assume no. of cars is x

no. of cars = x = 187950 / (toll price in euros)

P(x cars in 1 day) = [e^(-90,000*1)]*((90,000*1)^(x))/(x!)