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 17%
while that of the latter is only 13%.
If tips are normally distributed with a standard
deviation of 8%, what is the probability
that in a random sample of 11 tips recorded from waiters
and waitresses who introduce themselves and 11 tips from
waiters and waitresses who don't, the mean of the former
will exceed that of the latter?
Probability =