At a post office the waiting time is exponentially distributed with expected value 5 minutes. Find the probability that 10 clients will have to wait longer than 60 minutes. I know F(x) = 1-e^(-0.2x) but I don't know how to proceed.
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Possibly related: https://math.stackexchange.com/questions/655302/gamma-distribution-out-of-sum-of-exponential-random-variables – saulspatz Jan 27 '19 at 16:31
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There's a difference between "10 clients together wait longer than 60" and "10 clients each wait longer than 60". For the former indeed it's a Gamma distribution as saulspatz linked, and for the latter it's just $\left( e^{-0.2 x} \right)^{10}$ with $x = 60$. – Lee David Chung Lin Jan 28 '19 at 04:27