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A manager at a local manufacturing company has been monitoring the output of one of the machines used to manufacture small aluminum plates. Past data indicates that if the machine is operating "properly," the length of the plates produced by this machine can be modeled as being normally distributed with a mean of 117 centimeters and a standard deviation of 5.2 centimeters. Suppose 10 plates produced by this machine are randomly selected. What is the probability that the average length of these 10 plates will be between 116 and 120 centimeters when the machine is operating "properly?"

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