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    Normal Distribution/Standard Deviation - Shoe Sizes

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    Suppose the shoe size of workers is normally distributed, with a mean of 10.0 inches, and a standard deviation of 0.5 inch. A clueless shoe manufacturer is going to introduce a new line of shoes specifically for these workers. Assume that if the shoe size falls between two shoe sizes, you purchase the next larger shoe size. How many pairs of each of the following sizes should be included in a batch of 1,000 pair of shoes?
    a. 8.5 b. 9.0 c. 9.5 d. 10.0
    e. 10.5 f. 11.0 g. 11.5

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    Solution Preview

    a) P(x<=8.5) = P(z<(8.5-10)/0.5)=P(z<-3) = 0.50-0.4987=0.0013
    Number of pairs of size 8.5 = 0.0013*1000=1.3 roundoff we get 1.

    b) P(8.5<x<9.0) = P((8.5-10)/0.5<z<(9.0-10)/0.5)=P(-3<z<-2) = 0.4987-0.4772=0.0215
    Number of pairs of size 9.0 = 0.0215*1000=21.5 ...

    Solution Summary

    The solution uses normal distribution to determine the size of shoes to be produced.