The owner of the doughnut shop has been paying attention to the number of customers who come through the shop. She has worked out than on average, 112 customers walk in every 8 hour day.
She normally has another member of staff to help serve customers on each day, but on one particular day the staff member called in sick with little warning and no time to call for a replacement. Halfway through the day, the owner needs a 30 minute lunch break, and is forced to close the shop for this period of time. Assuming that customers arrive according to a Poisson process, what is the probability that more than 6 customers arrive during this lunch break?