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Each item produced in a certain factory is , independently, of acceptable quality with probability $0.95$. Approximate using a normal random variable the probability that at most 9 of the next 200 items are unacceptable.

Let $X$ equal to the number of items that are unacceptable.

Do I need the continuity correction here?

Should I set up the question as $P(X\leq9)$ or $P(X\leq10)$?

user59036
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1 Answers1

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The standard advice is to use the continuity correction. We are approximating the probability that our random variable is $\le 9$. So we find the probability that the approximating normal (mean $10$, standard deviation $\approx 3.08$) is $\le 9.5$.

Nowadays, the calculator or computer makes it relatively easy to calculate probabilities for the binomial distribution exactly. Such a calculation gives that the required probability is close to $0.4547$.

I believe that you will find that with the continuity correction, the normal approximation is pretty good. Without the continuity correction, not so good.

André Nicolas
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  • You are welcome. The continuity correction is somewhat a rule of thumb. One can produce examples in which using it gives a less accurate result than not using it. But in general it works fairly well. – André Nicolas Mar 11 '13 at 07:14