Question

In a given city, 6 % of all drivers get at least one parking ticket per year. A total of 80 drivers are randomly chosen in the city.
(i) State the binomial model. What is the probability that four will get at least one parking ticket in any given year? By applying Poisson approximation to the binomial distribution, analyze the same problem and comment on the results

Answer 1

Let X denotes the number of drivers who will get at least one parking ticket in any given year out of 80 selected drivers.

i) X ~ Binomial(80, 0.06)

The probability mass function of X is

The probability that four will get at least one parking ticket in any given year

ii) E(X)= 80*0.06 = 4.8

By applying Poisson approximation to the binomial distribution, we can write X ~ Poisson(4.8)

The probability mass function of X is

The probability that four will get at least one parking ticket in any given year