# Binomial Distribution

Merican air flight 2705 from N.Y. to San Francisco has seats for 340 passengers. An average of 7% of the people with reservations do not show up so American Air overbooks by accepting 355 reservations for the 340 seats. We can analyze this system by using a binomial distribution with N=355 and P=0.93 (the probability that a booked passenger does show up.)

A.) find the mean number of booked passengers that the airline should expect to show up for a flight? What is the standard deviation?

B.) find the probability that exactly 340 passengers show up for the flight

c.) find the probability that at least 341 passengers show up for the flight(in this case some passengers will be bumped from the flight) explain how you obtained your answer.

D.) use excel to create a probability histogram for the probabilities that correspond to x . or = to 305. use on the horizontal axis the values: x=305, 306...350. The vertical axis should display P(x).

E.)approximate a binomial distribution with a normal distribution. (If using a normal distribution in this way,the mean is the population mean and the standard deviation is the population Standard deviation.) Using a normal distribution, approximate the probability that the flight is overbooked: To do this, find P(x. or = to 340.5) Was this a good approximation? Compare to your answer in part B. include a supporting graph.

F.) Is the probability of overbooking small enough so that it doesnt happen very often, or does it seem too high so that changes should be made to make it lower? Thank you for helping me.

#### Solution Summary

The solution addresses - American air flight 2705 from N.Y. to San Francisco has seats for 340 passengers. An average of 7% of the people with reservations do not show up so American Air overbooks by accepting 355 reservations for the 340 seats. We can analyze this system by using a binomial distribution with N=355 and P=0.93 (the probability that a booked passenger does show up.)

A.) find the mean number of booked passengers that the airline should expect to show up for a flight? What is the standard deviation?

B.) find the probability that exactly 340 passengers show up for the flight

c.) find the probability that at least 341 passengers show up for the flight(in this case some passengers will be bumped from the flight) explain how you obtained your answer.

D.) use excel to create a probability histogram for the probabilities that correspond to x . or = to 305. use on the horizontal axis the values: x=305, 306...350. The vertical axis should display P(x).

E.)approximate a binomial distribution with a normal distribution. (If using a normal distribution in this way,the mean is the population mean and the standard deviation is the population Standard deviation.) Using a normal distribution, approximate the probability that the flight is overbooked: To do this, find P(x. or = to 340.5) Was this a good approximation? Compare to your answer in part B. include a supporting graph.

F.) Is the probability of overbooking small enough so that it doesnt happen very often, or does it seem too high so that changes should be made to make it lower? Thank you for helping me.