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Normal Probability

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Ayrshire cows average 47 pounds of milk a day with a standard deviation of 6 pounds. For Jersey cows the mean daily production is 43 pounds, with a standard deviation of 5 pounds. Assume that normal models describe milk production for these breeds.

One farmer has 20 jerseys, while a neighboring farmer has 10 Ayrshires. What's the probability that the neighboring farmer's herd average is at least 5 pounds higher than the average for the jersey herd?

I don't know how to combine the two to figure out the probability of the Ayrshires' herd average being at east 5 pounds higher than the average of the Jerseys.

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Solution Summary

The expert compares the probability of two statistics using a sample mean and standard deviation.

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If X and Y are normal variables then X-Y ~ N (μx - μy, √ (σx ^2/n1 + σy^2/n2))
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