Ayrshire cows average 47 pounds of milk a day with a standard deviationof 6 pounds. For Jersey cows the meandaily 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 probabilitythat 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.
Please see the attached file.
If X and Y are normal variables then X-Y ~ N (μx – μy, √ (σx ^2/n1 + σy^2/n2))
The expert compares the probability of two statistics using a sample mean and standard deviation.