A consumer product that has flourished in the last few years is bottled natural spring water.

Jon Thorne is the CEO of a company that sells natural spring water. He has requested a report of the filling process of the 24-ounce (710-milliliter) bottles to be sure that they are being properly filled. To check if the process needs to be adjusted, Emma Astrom, who monitors the process, randomly samples and weighs five bottles every 15 minutes for a 5-hour period. The data are contained in the data file Bottles.

a. Compute the sample mean, sample standard deviations for individual bottles, and the standard deviation of the sample mean for each sample.

b. Determine the probability that the sample means are below 685 milliliters if the population mean is 710.

c. Determine the probability that the sample means are above 720 milliliters.