Offwefly Airlines has a daily flight from Sacramento to Las Vegas with a capacit

Question

Offwefly Airlines has a daily flight from Sacramento to Las Vegas with a capacity of 100 passengers. On average, 15 ticket holders cancel their reservations at the last minute, so the company intentionally overbooks the flight. Cancellations can be described by a normal distribution with a standard deviation of 4.4. Profit per passenger is $52. If a passenger arrives but cannot board due to overbooking, the company policy is to provide compensation of $169.

What is the optimal probability of having one or more empty seats on the plane?

Explanation / Answer

Given, the flight overbooks all flights at 115 passengers per flight after looking at average cancellations.

Also given that,

Average number of cancellations=15 (mean)

Standard deviation= 4.4

So now we'll generate randon data, using excel. We'll take a Sample size of 50 flights. I have included the formula screenshot of excel; Increase the sample size as per your requirement.

For the situation given, there must be 16 or more cancellations per flight.

We'll run 10 simulations in excel.

Formula sheet:

Now, data generated:

The generated data we'll use for our analysis is in 4th column (D).

Using =countif(d3:d53,">15") we get number of counts when 16 or more passengers cancel flights.

We can then calculate probability.

On running this 10 times; we get countif in the range of 20 to 28.

On calculating probability:

So probability will be 0.48

Mean needed 15 Mean =AVERAGE(B3:B52) Std deviation needed 4.4 Standard dev =STDEV.P(B3:B52) Random Variables =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B3-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B4-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B5-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B6-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B7-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B8-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B9-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B10-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B11-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B12-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B13-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B14-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B15-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B16-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B17-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B18-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B19-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B20-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B21-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B22-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B23-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B24-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B25-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B26-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B27-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B28-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B29-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B30-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B31-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B32-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B33-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B34-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B35-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B36-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B37-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B38-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B39-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B40-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B41-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B42-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B43-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B44-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B45-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B46-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B47-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B48-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B49-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B50-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B51-$D$1)*$B$2/$D$2 =NORMINV(RAND(),$B$1,$B$2) =$B$1+(B52-$D$1)*$B$2/$D$2 Check mean =AVERAGE(D3:D52) Check std deviation =STDEV.P(D3:D52)

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