- #1

mathmari

Gold Member

MHB

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An insurance office has $2500$ contracts with mean annual profit (per contract) $\mu=330$ and standard deviation $\sigma=540$. Calculate the probability that the total annual profit is not more than $800000$.

I have one the following:

The annual total profit should be not more than $800000$, that means that per contract it shoulebe not more than $\frac{800000}{2500}=320$.

So $$Z=\frac{X-\mu}{\sigma}=\frac{320-330}{540}\approx -1.31 \\ P(Z\leq -1.31)=0.0968$$ Is that the correct probability?