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A cola-dispensing machine is set to dispense 8 ounces of cola per cup, with a standard...

A cola-dispensing machine is set to dispense 8 ounces of cola per cup, with a standard deviation of 0.7 ounce. The manufacturer of the machine would like to set the control limit in such a way that, for samples of 30, 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.

If the population mean shifts to 7.8, 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.)

If the population mean shifts to 8.7, 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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