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 18% while that of the latter is only 12%. If tips are normally distributed with a standard deviation of 10%, what is the probability that in a random sample of 13 tips recorded from waiters and waitresses who introduce themselves and 13 tips from waiters and waitresses who don't, the mean of the former will exceed that of the latter?
Probability =