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.
Accepted Solution
A:
We can solve this problem through exponential distribution. We have that,[tex]\mu = \frac{1}{\lambda} = 1100[/tex]clearing for \lambda we have[tex]\lambda = \frac{1}{1100}[/tex]The exponential distribution is given by,[tex]P(x) = 1-e^{-\lambda x}[/tex]a) We define our probability for x>4000, that is,[tex]P(x>4000) = 1- [1-e^{-\frac{4000}{1100}}][/tex][tex]P(x>4000) = e^{3.6363}[/tex][tex]P(x>4000) = 0.02634[/tex]b) We define our probability for x>1100, that is[tex]P(x>1100) = 1- [1-e^{-\frac{1100}{1100}}][/tex][tex]P(x>1100) = e^{-1}[/tex][tex]P(x>1100) = 0.3679[/tex]