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Chapter 6: Q. 87 (page 405)

87. Airport security The Transportation Security Administration (TSA) is responsible for airport safety. On some flights, TSA officers randomly select
passengers for an extra security check before boarding. One such flight had 76辫补蝉蝉别苍驳别谤蝉鈥�12in first class and 64in coach class. Some passengers were surprised when none of the 10 passengers chosen for
screening were seated in first class. Can we use a binomial distribution to approximate this probability? Justify your answer.

Short Answer

Expert verified

No binomial distribution to approximate this probability.

Step by step solution

01

Given information

One flight had 76passengers.12in first class and 64in coach class. Some passengers were surprised when none of the 10 passengers chosen for screening were seated in first class.

02

Explanation

A random variable has a binomial distribution if:

  • In terms of variables, there are two possible outcomes.
  • Each draw must be self-contained.
  • There are a set number of elements.

In probability, there is always a chance of success. Because each draw is not independent, persons are chosen without replacement, and the sample size is greater than 10%of the population, Xhas no binomial distribution.

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