At a certain coffee shop, all the customers buy a cup of coffee and some also buy a doughnut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 310 cups and a standard deviation of 24 cups. He also believes that the number of doughnuts he sells each day is independent of the coffee sales and is normally distributed with a mean of 170 doughnuts and a standard deviation of 12.

 What's the probability that on any given day he'll sell a doughnut to more than half of his coffee customers?