Calculating Binomial Probabilities - Suppose you work for an airline and you are taking reservations for a flight on an aircraft that has 152 seats. You know, based on historical flights trends, that if you sell a single ticket there is a 91% chance that the person with the ticket will actually show up for the flight. You decide to try to make a little extra money by overbooking your flight and you sell 160 tickets hoping that not more than 152 people will actually show up for the flight (note: this is a common business practice! Click here to watch a video that explains why)
Explain how this scenario meets the four requirements in the definition of a Binomial Distribution.
Identify what n and p are in this example
Use technology (StatCrunch, Statdisk, or Excel) to calculate the probability that if you sell 160 tickets for your flight, more passengers will show up than there are seats available (again, the plane has 152 seats total). Post an image of your technology output using the Insert/Edit Image feature in Blackboard (no attachments!)
Based on this probability, do you think it is a wise business practice to oversell your flight in this manner? Explain.

The value of n is fixed i.e. 160
The outcome has two possible values i.e. seats available or not
The chance that a person shows up is the same for each outcome i.e. p = 91%
Each observation is independent.

Identify n and p

The given parameters are:

n = 160

p = 0.91 i.e. 91%

x = 152

How to determine the probability?

The distribution is a binomial distribution, and it is calculated using:

[tex]P(x) = ^nC_x * p^x * (1 - p)^{n -x}[/tex]

The probability is represented as:

P(x > 152) = P(153) + ..... P(160)

Using a technology tool, we have:

P(x ≤ 152) = 0.02

Conclusion on the calculation

Probability values less than 0.25 are unlikely probabilities.

Because the probability value 0.02 is less than 0.25, then we can conclude that it is a wise business practice to oversell your flight in this manner.