Question

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. Should we use a binomial distribution to approximate this probability? Justify your answer.

Short answer

To approximate the probability yes or no, a binomial distribution is used.

Step-by-step solution

Given Information

There were 76 people on one such aircraft, 12 in first class and 64 in coach.

None of the ten passengers chosen for screening were sat in first class, which startled some passengers.

According to the given question

A binomial distribution describes the distribution of a random variable.

When there are two alternative outcomes for a variable, each draw must be independent of the preceding one.

A fixed number of components are drawn.

Because each draw is not independent of the previous ones and the sample size is greater than 10% of the population, the constant probability of success X does not have a binomial distribution.