A credit card company has been billing its millions of customers on the last day of each month, receiving payment on average 13 days later. It decides to experiment with the billing date, hoping to accelerate payments. A simple random sample of 500 customers is switched to a billing date in the middle of the month. The average length of time between billing and payments is the sample comes to 18.9 days, with a sample standard deviation of 5.3 days. Prepare a 98% confidence interval for the mean period between billing and payment for all customers if all of them were given the mid month billing date.