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Two made-up machines fill 500 g bags of rice…

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Two made-up machines fill $500\ \text{g}$ bags of rice. For machine P, the error of a bag is $-2\ \text{g}$ , $0\ \text{g}$ or $2\ \text{g}$ with probabilities $0.1$ , $0.8$ and $0.1$ . For machine Q, it is $-1\ \text{g}$ , $0\ \text{g}$ or $1\ \text{g}$ with probabilities $0.3$ , $0.4$ and $0.3$ . Both have a mean error of $0\ \text{g}$ . Find the standard deviation of each, and say which machine is more consistent.

Need a reminder? The key ideaShow

The variance is the weighted mean of the squared distances from $\mu$ , and the standard deviation is its square root:

\displaystyle \sigma^2 = \sum (x - \mu)^2 P(X = x) = E(X^2) - \mu^2.

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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