Question

A California water company has determined that the average customer billing is ​$1,100 per year and the amounts billed have an exponential distribution. a. Calculate the probability that a randomly chosen customer would spend more than ​$ 4,000. b. Compute the probability that a randomly chosen customer would spend more than the average amount spent by all customers of this company.

Answer 1

We can solve this problem through exponential distribution.

We have that,

`\mu = (1)/(\lambda) = 1100`

clearing for \lambda we have

`\lambda = (1)/(1100)`

The exponential distribution is given by,

`P(x) = 1-e^(-\lambda x)`

a) We define our probability for x>4000, that is,

`P(x>4000) = 1- [1-e^{-(4000)/(1100)}]`

`P(x>4000) = e^(3.6363)`

`P(x>4000) = 0.02634`

b) We define our probability for x>1100, that is

`P(x>1100) = 1- [1-e^{-(1100)/(1100)}]`

`P(x>1100) = e^(-1)`

`P(x>1100) = 0.3679`