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A made-up machine fills bags of flour. The masses follow a normal curve with standard deviation 4…

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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 machine fills bags of flour. The masses follow a normal curve with standard deviation $4\ \text{g}$ , and the mean can be set. The label says $500\ \text{g}$ , and only $2\%$ of bags may be lighter than that. Find the z-score with $2\%$ of the area to its left. Then find the mean that the machine must be set to. Give the z-score to three decimal places and the mean to one.

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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