1) 5.31 Bottling an energy drink. A bottling company uses a filling machine to fill cans with an energy drink. The cans are supposed to contain 250 milliliters (ml). The machine, however, has some variability, so the standard deviation of the volume is = 0.4 ml. A sample of five cans is inspected each hour for process control purposes, and records are kept of the sample mean volume. If the process mean is exactly equal to the target value, what is the mean and standard deviation of the numbers recorded?

5.33 Can volumes. Averages are less variable than individual observations. It is reasonable to assume that the can volumes in Exercise 5.31 vary according to a Normal distribution. In that case, the meanxof an SRS of cans also has a Normal distribution.

a)Make a sketch of the Normal curve for a single can. Add the Normal curve for the mean of an SRS of five cans on the same sketch.

b)What is the probability that the volume of a single randomly chosen can differs from the target value by 0.1 ml or more?

c)What is the probability that the mean volume of an SRS of five cans differs from the target value by 0.1 ml or more?