A restaurant gets an average of 5.3 complaints per day from its patrons. Use the Poisson distribution
formula to find the probability that on a given day
the restaurant will receive
a. exactly 4 complaints.
b. between 2 and 6 complaints.

a. 16.41%

b. 68.57%

Step-by-step explanation:

We have that the poisson formula is as follows:

P (x = x) = (e ^ l) * (l ^ x) / x!

In this case l = 5.3

a. 4 exactly therefore x = 4, replacing:

P (x = 4) = (e ^ 5.3) * (5.3 ^ 4) / 4!

P (x = 4) = 0.1641

That is, the probability is 16.41%

b. between 2 and 6 complaints.

P (2 <= x <= 6) = P (x = 2) + P (x = 3) + P (x = 4) + P (x = 5) + P (x = 6)

replacing:

P (2 <= x <= 6) = (e ^ 5.3) * (5.3 ^ 2) / 2! + (e ^ 5.3) * (5.3 ^ 3) / 3! + (e ^ 5.3) * (5.3 ^ 4) / 4! + (e ^ 5.3) * (5.3 ^ 5) / 5! + (e ^ 5.3) * (5.3 ^ 6) / 6!

P (2 <= x <= 6) = 0.6857

In other words, the probability is 68.57%