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An airfreight company has various classes of freight. In one of these classes the average weight of packages is $10 \mathrm{~kg}$ and the variance of the weight distribution is $9 \mathrm{~kg}^{2}$. Assuming that the package weights are independent (it is not the case that a single company is sending a large number of identical packages, for instance), estimate the probability that 100 packages will have total weight more than $1020 \mathrm{~kg}$.
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The central limit theorem says $\sum W_{i}$ is approximately $N\left(1,000,30^{2}\right)$ so that $P\left(\sum W_{i}>1,020\right) \approx$ $P[Z>(1,020-1,000) / 30=0.67]=0.251$
by Diamond (80,728 points)

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