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]
