Question

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 $76$passengers—$12$in first class and $64$in 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

No binomial distribution to approximate this probability.

Step-by-step solution

Given information

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

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, $X$has no binomial distribution.