Question

Airlines typically overbook flights because usually several passengers don’t show up. Assume that one airline flies jets that seat 200 passengers, and with overbooking, the numbers of passengers that show up are approximately normally distributed with mean 182 and standard deviation 8.

1. (a) What is the probability that there will not be enough seats on any given flight?

Hint: How many people need to show in order for there not to be enough seats?

1. (b)What is the 96^th percentile of the number of people that show up for the flight?

Given the answer above (in part b) we can say that 96% of the time there will be

at least ____________________ empty seats on any given flight.

Answer 1

Solution:-) We have , X is number of passengers.

(a) The probability that there will not be enough seats on any given flight when the number of passengers are greater than 200.

(b)  The 96^th percentile of the number of people that show up for the flight is calculated by R

C =196.0055  

Given the answer above (in part b) we can say that 96% of the time there will be

at least 200-196 =4 empty seats on any given flight.

The R output is