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A research group publishes 20 separate 95% intervals over a year, each from its own independent…

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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 research group publishes $20$ separate 95% intervals over a year, each from its own independent random sample. Find the expected number of intervals that miss the true value. Find the probability that all $20$ catch their true values. Find the probability that at least one misses. Give the probabilities to four decimal places.

Need a reminder? The key ideaShow

In the long run, $95\%$ of the intervals made this way catch the true value. Multipliers: $1.645$ , $1.96$ and $2.576$ for $90\%$ , $95\%$ and $99\%$ . For a large sample, the interval for a mean is $\bar x \pm 1.96\dfrac{s}{\sqrt n}$ .

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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