On a given GNV$-$ATL flight, there are $200$ seats and each seat is sold at an average ticket

price of $ $250.$ It has been observed that on most days in the past month, the flight rarely

approaches $100\%$ occupancy since there are passenger no$-$shows. Hence, the airline

decides to overbook flights. The airline manager assigned the task of determining the

number of seats to overbook on this flight starts by estimating no$-$shows using historical

information. However, she encounters an interesting conundrum: the mean no$-$shows

changes based on the rate offered to customers with a confirmed booking who are denied

a seat on the flight $($referred to as the service denial rate$).$

She would like to start by analyzing the impact of an overbooking policy by considering

three specific service denial rates:

$1.$ Service Denial Rate $=$$ $400.$ No$-$shows for this denial rate are uncertain and

normally distributed with a mean $=25$ and standard deviation $\backslash$sigma $=7.$

$2.$ Service Denial Rate $=$$ $500.$ No$-$shows for this denial rate are uncertain and

normally distributed with a mean $=22$ and standard deviation $\backslash$sigma $=8.$

$3.$ Service Denial Rate $=$$ $600.$ No$-$shows for this denial rate are uncertain and

normally distributed with a mean $=19$ and standard deviation $\backslash$sigma $=9.$