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?

Answer:a) 0.16873b) 0.35945c) 0.1563Step-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! = 0.16873b) 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!= 0.35945c) 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