A cola-dispensing machine is set to dispense 9.00 ounces of cola per cup, with a standard deviation of 1.00 ounce. The manufacturer of the machine would like to set the control limit in such a way that, for samples of 36, 5% of the sample means will be greater than the upper control limit, and 5% of the sample means will be less than the lower control limit.
a. At what value should the control limit be set?
b. If the population mean shifts to 8.6, what is the probability of detecting the change?
c. If the population mean shifts to 9.6, what is the probability of detecting the change?