Question

A particular intersection in a small town is equipped with a surveillance camera. The number of traffic tickets issued to drivers passing through the intersection follows the Poisson distribution and averages 3.9 per month.

a) what is the probability that 5 traffic tickets will be issued at the intersection next month?

b) what is the probability that 3 or fewer traffic tickets will be issued at the intersection next month?

c) what is the probability that more than 6 traffic tickets will be issued at the intersection next month?

Answer 1

Solution :

Given that ,

mean = = 3.9

Using poisson probability formula,

P(X = x) = (e^- * ^x ) / x!

(a)

P(X = 5) = (e^-3.9 * 3.9⁵⁾ / 5! = 0.1522

Probability = 0.1522

(b)

P(X 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

=  (e^-3.9 * 3.9⁰⁾ / 0! +  (e^-3.9 * 3.9¹⁾ / 1! +  (e^-3.9 * 3.9²⁾ / 2! +  (e^-3.9 * 3.9³⁾ / 3!

= 0.45325

Probability = 0.45325

(c)

P(X > 6) = 1 - P(X )

= 1 - {P(X = 0) + .......+ P(X = 6)}

= 1 - 0.8995

= 0.1005

Probability = 0.1005