Weights of elephants approximately follow an exponential distribution with the mean of 2.5 tons. One hundred elephants are being transported on a ship that has a cargo limit of 300 tons. What is the chance this ship will sink?
I think i kind of understand this problem but unsure.
lambda = 1/2.5 = 0.40
exp. dist. x < 300
so 1- e^-(0.40)(100) = 1 so it will sink?
I would use the normal approximation, with n=100.
By the Central Limit Theorem
NOW use your distribution..
You have a mean of 2.5 and a variance of 2.5 via the exponential distribution...
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If you don't want to approximate this, then use that fact that a sum of iid exponentials is a gamma.
Either way you need to calculate