Prairie Flower Cereal, Inc., is a small but growing producer of hot and ready-to-eat breakfast cereals. The company was started in 1910 by Gordon Thorson, a successful grain farmer. You have been asked to test the cereal-packing process of 18-ounce (510-gram) boxes of sugar-coated wheat cereal. Two machines are used for the packaging process. Twenty samples of five packages each are randomly sampled and weighed. The data are contained in the file Sugar Coated Wheat.

a. Compute the overall sample mean, sample variance, and variance of the sample means for each machine.

b. Determine the probability that a single sample mean is below 500 if the process is operating properly for each machine.

c. Determine the probability that a single sample mean is above 508 if the process is operating properly for each machine.

d. Using your statistical computer package, obtain 20 random samples of size n = 5 packages for each machine and compute the sample mean for each sample. Count the number of sample means that are below 500 and the number that are above 508.