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There's a question I'm not really sure if I did it right or even understand what its trying to say.

There is a coin which produces heads with an unknown probability $p$. How many times should we throw this coin if the proportion of heads is to lie within $0.05$ of $p$ with probability at least $0.9$? Hint: Answer is not complete if it relies on $p$ and do not worry about continuity correction.

This question comes from a chapter about binomial normal approximation.

So far I know I have a $\mathcal B(n,p)$ and I need to find the number of $n$ so that $P(c/n \le 0.05*p) \ge 0.9$ with $c$ as the number of heads? I'm not sure if this is right.

In turn $P( c \le 0.05np ) \ge 0.9$

So I'll normalize the binomial such that $$ P\bigg( Z \le \frac{0.05np - n*p}{np(1-p)} +0.5\bigg) \ge 0.9 $$ with $0.5$ as the continuity correction.

Am I on the right track? I thought about using confidence intervals but we haven't discussed about that in the chapter or lecture.

gung - Reinstate Monica
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user42668
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  • possible duplicate of [How often do you have to roll a 6-sided dice to obtain every number at least once?](http://stats.stackexchange.com/questions/48396/how-often-do-you-have-to-roll-a-6-sided-dice-to-obtain-every-number-at-least-onc) – Sycorax Mar 29 '14 at 02:20
  • You might some advantage in looking [here](http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval) (perhaps starting with the Wilson score interval). Given the question tells you not to worry about the continuity correction, why did you? – Glen_b Mar 29 '14 at 06:18
  • Well we didn't really learn about confidence intervals in the chapter and the lecture. The only thing we were taught about Binomial Normal Approximation was the continuity correction. – user42668 Mar 29 '14 at 06:44

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