Question

Complaints about an Internet brokerage firm occur at a rate of 6 per day. The number of complaints appears to be Poisson distributed.

A. Find the probability that the firm receives 7 or more complaints in a day.

Probability =

B. Find the probability that the firm receives 33 or more complaints in a 5-day period.

Probability =

Answer 1

a)
Here, λ = 6 and x = 6
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X > 6) = 1 - P(X <= 6).
P(X > 6) = 1 - (6^0 * e^-6/0!) + (6^1 * e^-6/1!) + (6^2 * e^-6/2!) + (6^3 * e^-6/3!) + (6^4 * e^-6/4!) + (6^5 * e^-6/5!) + (6^6 * e^-6/6!)
P(X > 6) = 1 - (0.0025 + 0.0149 + 0.0446 + 0.0892 + 0.1339 + 0.1606 + 0.1606)
P(X > 6) = 1 - 0.6063
= 0.3937

b)
Here, λ = 6*5 = 30 and x = 33

P(X > 32) = 1 - P(X <= 32)
= 1 - 0.6845
= 0.3155