In: Statistics and Probability
Potatoes - Samples: Assume the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.2 ounces. He bags his potatoes in groups of 6. You buy a bag and the total weight is 42 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. (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) Were you luck or unlucky? Why?