Please provide a detailed step by step solution. This is from the topic unknown demand in inventory and warehouse management

An airline must decide how many seats it needs to book on a popular route between Islamabad and Lahore. How many seats should the airline book? The aeroplane has 250 seats for passengers. History has shown that when the same aeroplane is fully booked, the number of last-minute cancellations has a mean of 7 and a standard deviation of 4. The average price of the ticket is $120. When the aeroplane is overbooked, the policy is to find a seat on an alternate flight for the passenger, which will cost the airline $380($220 for booking on such late notice and $160 as compensation to the passenger for the inconvenience caused)