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A made-up survey asks 400 people a question, and each says yes with probability 0.5, independently…

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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 survey asks $400$ people a question, and each says yes with probability $0.5$ , independently. Find the mean and the standard deviation of the number who say yes. Use the normal curve with a continuity correction, so that $220$ or more becomes $219.5$ or more, to estimate the probability of $220$ or more yes answers. Give four decimal places.

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

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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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