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Normal Probability Distribution Question?

You breed miniature mules (father is a miniature donkey, mother is a miniature horse) and currently have as breeding stock 1 jack (male donkey) and 7 mares (female horses) and these are able to produce 7 mule foals (baby mules) for you every year. You would like to produce miniature mules that are quite small, but unfortunately there is considerable variation in the sizes of mule offspring produced even from the same set of parents. Based on the best information you can obtain, the heights of the mules you produce are normally distributed with a mean height of 32.5 inches and a standard deviation of 1.25 inches. Any mule less than or equal to 32 inches can be sold for a high price and any mule greater than 32 inches in height can be sold only for a lower price.

Assuming that your model (normal distribution with parameters as stated above) of mule heights is accurate, and also assuming that there is no limit to the level of precision with which you can measure the mules, what is the probability that any given mule will turn out to be one you can sell at the high price?

1 Answer

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  • 1 decade ago
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    The price limit represents a (32.0-32.5)/1.25 = -0.4 sigma point, so

    most of your stock will be at the lower price. If you look up the

    -0.4 sigma point in a normal probability table, you'll see this

    represents 34.46%. So the probability of the higher price is 0.3446.

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