13. The quality assurance department for Pepsi Distributors, Inc. maintains meticulous records on the bottling line for two-liter Pepsi bottles. Records indicate that the process follows the normal probability distribution with a mean amount per bottle of 2.01 liters and a standard deviation of 0.025 liters. The foreman randomly selects 25 bottles from the bottling line and determines that the mean amount per bottle is 2.005 liters.
a. Compute the sampling error.
b. Compute the standard error of the sampling distribution of sample means.
c. Compute the probability that the sample of 25 bottles would have a mean of 2.005 liters or more.
14. Suppose the foreman in Problem 13 selects a second sample of 16 bottles and determines that the mean is 1.994 liters. Compute the probability that the sample of 16 bottles would have a mean of 1.994 liters or more.
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The solution discusses sampling and standard errors for Pepsi distributors.