A cola-dispensing machine is set to dispense 9 ounces of cola per cup, with a standard deviation of 0.8 ounce. The manufacturer of the machine would like to set the control limit in such a way that, for samples of 50, 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? (Round z values to two decimal places. Round your answers to 2 decimal places.) b. If the population mean shifts to 8.6, what is the probability that the change will not be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.) c. If the population mean shifts to 9.4, what is the probability that the change will not be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
A cola-dispensing machine is set to dispense 9 ounces of cola per cup, with a standard deviation of 0.8 ounce. The manufacturer of the machine would like to set the control limit in such a way that, for samples of 50, 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? (Round z values to two decimal places. Round your answers to 2 decimal places.)
b. If the population mean shifts to 8.6, what is the probability that the change will not be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
c. If the population mean shifts to 9.4, what is the probability that the change will not be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
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