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 averages 4.4 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?

a) 0.16873

b) 0.35945

c) 0.1563

Step-by-step explanation:

The Poisson distribution is a distribution that expresses what is the probability of a given number of events occurring in a fixed interval of time when these events occur with a known constant rate.

In this problem we know that the tickets issued through this intersection averages 4.4 per month. Therefore, we could use Poisson distribution.

The formula for an event with a Poisson probability distribution is given by:

P (n events in an interval) = λⁿe^ (-λ) / n! where λ is the average number of events in the interval.

In this problem we have that λ = 4.4

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

P (5 tickets) = 4.4⁵e⁻⁴⁻⁴ / 5! = 0.16873

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

P (x≤3) = P (0 tickets) + P (1 ticket) + P (2 tickets) + P (3 tickets)

= 4.4⁰e⁻⁴⁻⁴ / 0! + 4.4¹e⁻⁴⁻⁴ / 1! + 4.4²e⁻⁴⁻⁴ / 2! + 4.4³e⁻⁴⁻⁴ / 3!

= 0.35945

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

P (x > 6) = 1 - P (x≤6) = 1 - (P (x=0) + P (x=1) + P (x=2) + P (x=3) + P (x=4) + P (x=5) + P (x=6)) * But we already calculated all these probabilities except for P (x = 4) and P (x = 6)

= 1 - (0.3595 + P (x=4) + 0.16873 + P (x=6))

=1 - (0.3595 + 4.4⁴e⁻⁴⁻⁴ / 4! + 0.16873 + 4.4⁶e⁻⁴⁻⁴ / 6!)

= 0.1563