Question: A grocery store sells apples in boxes. Each box has 12 apples. The apples vary in size, but all boxes have the same label that

A grocery store sells apples in boxes. Each box has 12 apples. The apples vary in size, but all boxes have the same label that says the net weight of the box is 46 oz and are sold at the same price.

  • Suppose workersnever weightthe boxes, but justrandomlyput 12 apples in each box.Should we worry that some boxes are lighter than 46 oz?
  • To put the question in context, suppose the weight of an apple follow a normal distribution, X ~ N(4, 0.2).What's the probability that the total weight ofa boxis below 46 oz?That is equal to ask:What's the probability that the average weight of the 12 apples is below 3.833 oz (= 46/12)?

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