Assignment:
A cola dispensing machine is set to depense 9 ounces per cup with a standard deviation of .5 oz. The manufacturer would like to set the control limits so that for samples of 16, 5% of the sample means will be greater than the upper limit and 5% of the sample means less than the lower limit.
a. At what values should the control limits be set
b. What is the probability a shift in the mean to 8.8 ounces will be detected
c. What is the probability a shift in the mean to 9.1 ounces will not be detected?
Provide complete and step by step solution for the question and show calculations and use formulas.