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State any assumptions you are making in using this model.

Question

State any assumptions you are making in using this model.

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Solution

In using the hypergeometric distribution model for this scenario, the following assumptions are made:

  1. Each bin is either from production line 1 or production line 2, and each bin is either red or not red. There are no other categories or possibilities.

  2. The bins are selected randomly. This means that each bin has an equal chance of being selected in the sample of 10 red bins.

  3. The selection of each bin is independent of the selection of any other bin. The outcome of one selection does not influence the outcome of any other selection.

  4. The total number of bins (120) and the sample size (10) are known and fixed.

  5. The number of red bins in the total population and the number of red bins from production line 1 in the population are unknown, but they are fixed and do not change during the selection process.

  6. The bins are selected without replacement. This means that once a bin is selected, it is not returned to the population and cannot be selected again.

  7. The population size is large enough relative to the sample size, so that the sampling without replacement can be approximated by the hypergeometric distribution.

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