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A made-up factory claims that 10% of its light bulbs fail a strength test…

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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 factory claims that $10\%$ of its light bulbs fail a strength test. An inspector tests $900$ bulbs, and $117$ of them fail. Find the share that failed. If the claim were true, the share would land within a band around $0.1$ in about $95$ runs out of $100$ . Find the half-width of the band and its two ends. Does the test fit the claim?

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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