Economic statistics

The number of monthly hacking attempts on a computer network is a Poisson-
distributed random variable with λ = 1.8 . What is the probability that the network
will function a month

1. without a hacking attempt; and,

2. with only one hacking attempt?

The number of customer assistance calls a software company gets per day is a
Poisson-distributed random variable with λ = 5.5 . What is the probability that on
any given day the company will receive only four calls?

The number of inquiries received in response to an ad placed on the Internet for a
house for sale is a Poisson-distributed random variable with λ = 4.4 . What are the
probabilities that the seller will receive

1. only two inquiries;

2. only three inquiries; and,

3. at most three inquiries?

The number of loan applications that a bank gets per day is a Poisson-distributed
random variable with λ = 7.5 . What are the probabilities that on any given day the
bank will receive

1. exactly six applications;

2. at most four applications;

3. at least eight applications; and,

4. anywhere from five to ten applications?