Z-Score And Normal Distribution Essay Example

Mathematics

Z –Score and Airline Overbooking
Z-score gives a statistical indication of a score’s relationship to the mean of a group of scores. A Z-score of zero indicates that the score is the same as the mean.
Airlines deal with no-show uncertainties using probabilistic models involving z-scores. They assume that no-show forecasts would form a Gaussian probability distribution. Using the properties of the normal distribution, they create an overbooking model that would keep denied bookings (DB) to an airline-specified target level, with a specified level of confidence. The level of confidence is determined by taking Z-score into account. For instance, if an airline wishes for a 95% confidence level, it would take into account the Z-Score of 1.645. Accordingly, a probabilistic model would be: AU = CAP/ (1 – NSR + 1.645 STD), where
AU = Authorized capacity, the maximum number of bookings the airline accepts.
CAP = physical capacity of seats.
NSR = No show rate.
1.645 is a Z-score for 95% level of confidence in a one-tailed normal distribution.
STD = Standard deviation of the sample
If the Z-Score were zero, the model would revert to becoming deterministic, where there would be equal chances of denied bookings as well as vacant seats (Belobaba, Odoni & Barnhart, 2009, p.93-95).

Application of Normal Distribution to Flight Deck Design

Flight decks of aircraft need to be designed taking into account the height of human beings likely to operate the aircraft. While it would be impractical to consider the entire range of human heights, a normal distribution is used, and the flight deck is designed for a defined percentile range of heights, arm reach and leg length of the intended population. Accordingly, the height of seats and distances to various controls are designed, so that human beings falling in the intended percentile range can operate the aircraft (Kapur, Sishta, Nayar, Mohalanobish & Kang, 2007).
Apart from flight deck design, central tendencies are also applied in deciding upon the layout of passenger seats. The distance between the seats needs to be such that the legs of passengers can be accommodated. Anthropometric data is used to determine a defined percentile of the normally distributed human leg lengths, and the seats are spaced accordingly.

References

Belobaba, P., Odoni, A., & Barnhart, C. (Eds.) (2009). The global airline industry. Sussex: Wiley. Retrieved 01 Feb 2015 from https://books.google.co.in/books?id=BRtDl0CJpQIC&pg=PA95&lpg=PA95&dq=how+do+z+scores+help+in+airline+overbooking&source=bl&ots=kzq9s0FTtK&sig=CgIIWHUhiUyjjhFRX--SYG8Bo7s&hl=en&sa=X&ei=DZTNVOfvCebumgX9x4HQBQ&ved=0CCQQ6AEwAQ#v=onepage&q=how%20do%20z%20scores%20help%20in%20airline%20overbooking&f=false
Kapur, R.R., Sishta, M.K., Nayar, G.S., Mohalanobish, U.S. & Kang, G.B.S. (2007). Aircraft-aircrew anthropometric compatibility assessment. Indian Journal of Aerospace Medicine Commemorative Volume: 48-50. Retrieved 01 Feb 2015, from http://medind.nic.in/iab/t07/s1/iabt07s1p47.pdf
Vink, P., & Brauer, K. (2011). Aircraft interior comfort and design. Retrieved 01 Feb 2015, from http://www.cao.ir/portal/File/ShowFile.aspx?ID=daca31b8-4beb-4e9e-933b-fa00ac3b41d2