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In a made-up town, 40% of adults have a library card…

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

In a made-up town, $40\%$ of adults have a library card. A survey picks $8$ adults at random from the whole town. Let $X$ be the number with a card. Find $P(X = 3)$ and $P(X \le 1)$ . Find the mean and the standard deviation of $X$ . Give four decimal places for the probabilities and three for the standard deviation.

Need a reminder? The key ideaShow

For $X \sim B(n, p)$ :

\displaystyle P(X = k) = \binom{n}{k}p^k(1 - p)^{n-k}, \qquad \mu = np, \qquad \sigma = \sqrt{np(1 - p)}.

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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