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Times for a made-up 3 km fun run follow a normal curve with mean 14.5 minutes and standard…

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

Times for a made-up $3\ \text{km}$ fun run follow a normal curve with mean $14.5$ minutes and standard deviation $1.2$ minutes. The fastest $10\%$ of runners win a medal. Below which time must a runner finish to win a medal? Give two decimal places.

Need a reminder? The key ideaShow

Turn a value into a z-score, then use the standard normal area $\Phi$ :

\displaystyle z = \frac{x - \mu}{\sigma}, \qquad P(X < x) = \Phi(z).

Backwards: $x = \mu + z\sigma$ .

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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