Question: The members of a private golf club have handicaps that are normally distributed with mean 15 and standard deviation 3.5. In a particular event, foursomes are chosen by grouping four players chosen at random from the club. The handicap of the foursome is the arithmetic average of the handicaps of the four players comprising the foursome. In what proportion of the foursomes will the handicap of the foursome be less than 10 or more than 20?
(Hint: The standard deviation of the average of four independent identically distributed random variables is exactly half the standard deviation of one of them.)