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The number of items handed in to the Lost Property Office of a busy railway station each day is a $Poi(16)$ random variable on a weekday (Monday to Friday), a $Poi(22)$ random variable on a Saturday and a $Poi(11)$ random variable on a Sunday. The numbers of items handed in to the office on different days are independent.

Use a Normal approximation to find the approximate probability that no more than $100$ items in total are handed in to this Lost Property Office next week (Sunday to Saturday, inclusive).

About the question above, is there any methods to get the normal approximation by three distributions?

alex.wang
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  • If $X$ is the number of items handed into the lost property office in a given week, then $X\sim \text{Poisson}(113)$ which is approximately $\mathcal{N}(113,113)$ –  Nov 18 '21 at 00:21
  • Can you explain a little about why the parameter would be $16\times 5+22+11$? Is there any theorem to get it? – alex.wang Nov 18 '21 at 00:25
  • https://math.stackexchange.com/questions/221078/poisson-distribution-of-sum-of-two-random-independent-variables-x-y –  Nov 18 '21 at 00:37

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