Potatoes - Samples: Assume the weights of Farmer Carl\'s potatoes are normally d

Question

Potatoes - Samples: Assume the weights of Farmer Carl's potatoes are normally distributed with a mean of 7.0 ounces and a standard deviation of 1.1 ounces. He bags his potatoes in groups of 6. You buy a bag and the total weight is 36 ounces. Here we determine how lucky or unlucky you are. (a) What is the mean potato weight in your bag of 6? Enter your answer to 1 decimal place. ounces (b) If 6 potatoes are randomly selected, find the probability that the mean weight is less than the mean found in your bag. Round your answer to 4 decimal places. (c) Which statement best describes your situation? You got lucky with such a generous amount of potato your bag. You got extremely unlucky because the probability of getting a bag weighing less than yours is about 0.01%. This is not particularly unusual because the mean weight in your bag is only 1 ounce below the mean of all Carl's potatoes. This is an unusually small amount of potatoes. You are unlucky because the probability of getting a bag weighing less than yours is only about 1.3%

Explanation / Answer

from central limit theorum

a) mean potato weight in your bag of 6=36/6=6 ounce

b) for n=6 potatoes std error of mean =std deviaitron/(n)1/2 =0.449

hence P(X<6)=P(Z<(6-7)/0.449)=P(Z<-2.2268)=0.01298

c)

You are unlucky because the probability of getting a bag weighing less than yours is only about 1.3%

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