Many bulk productssuch as iron ore, coal, and raw sugarare sampled for quality by a

Chapter 7, Problem 7.56

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Many bulk productssuch as iron ore, coal, and raw sugarare sampled for quality by a method that requires many small samples to be taken periodically as the material is moving along a conveyor belt. The small samples are then combined and mixed to form one composite sample. Let Yi denote the volume of the ith small sample from a particular lot and suppose that Y1, Y2,..., Yn constitute a random sample, with each Yi value having mean (in cubic inches) and variance 2. The average volume of the samples can be set by adjusting the size of the sampling device. Suppose that the variance 2 of the volumes of the samples is known to be approximately 4. The total volume of the composite sample must exceed 200 cubic inches with probability approximately .95 when n = 50 small samples are selected. Determine a setting for that will allow the sampling requirements to be satisfied.