A cola-dispensing machine is set to dispense 9.00 ounces of cola per cup, with a standard deviation of 1.00 ounces. The manufacturer of the machine would like to set the control limit in such a way that for samples of 36,5 percent of the sample means will be greater than the upper control limits, and 5 percent of the sample mean will be less than the lower control limit.
a. At what value should the control limit be set?
b. What is the probability that if the population mean shifts to 8.9, this change will not be detected?
c. What is the probability that if the population mean shifts to 9.3, this change will not be detected?