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 4.5 per month

.a. What is the probability that 55 traffic tickets will be issued at the intersection next​ month?

b. What is the probability that 33 or fewer traffic tickets will be issued at the intersection next​ month?

c. What is the probability that more than 66 traffic tickets will be issued at the intersection next​ month?

a. The probability of exactly 55 traffic tickets is

​(Round to four decimal places as​ needed.)

b. The probability of 33 or fewer traffic tickets is

​(Round to four decimal places as​ needed.)

c. The probability of more than 66 traffic tickets is

Answer 1

Solution:-

a) The probability of exactly 55 traffic tickets is 0.0000.

u = 4.5

x = 55

By applying poisons distribution:-

P(x; μ) = (e^-μ) (μ^x) / x!

P(x = 55) = less than 0.00001

b) The probability of 33 or fewer traffic tickets is 0.9999.

u = 4.5

x = 33

By applying poisons distribution:-

P(x; μ) = (e^-μ) (μ^x) / x!

P(x < 33) = 0.9999

c) The probability of more than 66 traffic tickets is 0.0000.

u = 4.5

x = 33

By applying poisons distribution:-

P(x; μ) = (e^-μ) (μ^x) / x!

P(x > 66) = 0.0000