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The manager of a restaurant believes that waiters and waitresses who introduce themselves by telling customers...

The manager of a restaurant believes that waiters and waitresses who introduce themselves by telling customers their names will get larger tips than those who don't. In fact, she claims that the average tip for the former group is 16% while that of the latter is only 13%. If tips are normally distributed with a standard deviation of 10%, what is the probability that in a random sample of 12 tips recorded from waiters and waitresses who introduce themselves and 12 tips from waiters and waitresses who don't, the mean of the former will exceed that of the latter?

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