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A fair coin is tossed 400 times. Find the half-width of the band that holds the share of heads in…

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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 fair coin is tossed $400$ times. Find the half-width of the band that holds the share of heads in about $95$ runs out of $100$ . Then give the lowest and highest share in the band, and the lowest and highest number of heads.

Need a reminder? The key ideaShow

In about $95$ runs out of $100$ , the share of successes in $n$ tries lands within $2\sqrt{p(1-p)/n}$ of the probability $p$ . For a fair coin this is $\dfrac{1}{\sqrt{n}}$ .

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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