# How can I get a binomial probability when $n$ is large?

The question is this:

A shipment contains $400$ boxes of components. A shipment is returned if $> 90$ boxes are rejected. History shows that $20\%$ of boxes are usually rejected. What is the probability of a shipment being returned?

I tried to use normal approximation; however I don't have standard deviation or sample deviation. How can I solve this?

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I presume that each component box is rejected independently w.p. $20\% = .2$. Then the number of rejected components is a binomial $\mathrm{Bin}(400, .2)$. Can you go from here? –  Srivatsan Nov 26 '11 at 21:06

The standard deviation of a binomial is $\sqrt{n p (1-p)}$. Use this along with the normal approximation to solve your problem.

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