1) Suppose that the fill-volume of water botles is normally distributed with a mean of 10.0 oz. and a standard deviation of 0.25 oz.

What is the probability that the fill-volume is within one standard deviation of its mean?

What is the probability that the fill-volume is between 10.0 and 10.125 oz.?

2)

In statistical quality control, samples are selected from production and various quality characteristics are measured in order to check that the process is "in control". Suppose that a bottling process is intended to fill bottles with, on average, 21 fluid ounces (fl. oz.) of beverage. Variation around the mean follows a Normal distribution with a standard deviation of 0.5 fluid ounces.

What is the probability that the sample mean fill-level for the 25 bottles will exceed 21.2 fl. oz. ?

If a technician samples n = 25 bottles (when the process is in control) and measures the volume of beverage in each, what is the standard deviation of the mean?

Find c such that the probability that the sample mean exceeds c when the process is in control is .05.