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A made-up clinic finds that 10% of its patients need a second visit…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A made-up clinic finds that $10\%$ of its patients need a second visit. For a sample of $80$ patients, find $np$ , and decide whether the number needing a second visit is close to normal. Then find the smallest sample size for which both $np$ and $n(1 - p)$ are at least $10$ .

Need a reminder? The key ideaShow

$B(n, p)$ is close to $N\!\left(np, \sqrt{np(1 - p)}\right)$ when $np \ge 10$ and $n(1 - p) \ge 10$ . Skewed or bounded data are often not normal.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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