A pollster claims that the mean amount spent on Christmas gifts by an American family is $927 with a standard deviation of $200. What is the probability that the mean amount spent on Christmas gifts...

 A pollster claims that the mean amount spent on Christmas gifts by an American family is $927 with a standard deviation of $200.  What is the probability that the mean amount spent on Christmas gifts for a sample of 500 families differs from the population mean by less than $15?