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A made-up factory cuts pipes to a length of 2000 mm…

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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 cuts pipes to a length of $2000\ \text{mm}$ . The lengths follow a normal curve with mean $2000\ \text{mm}$ and standard deviation $1.5\ \text{mm}$ . A pipe is rejected if it is more than $3\ \text{mm}$ too long or too short. Find the z-score of the upper limit, the share of pipes rejected, and about how many of $2000$ pipes are rejected. Give four decimal places for the share.

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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