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. TSA officers selected an SRS of $10$passengers for screening. Let $\stackrel{⏜}{p}$ be the proportion of first-class passengers in the sample.

a. Is the 10% condition met in this case? Justify your answer.

b. Is the Large Counts condition met in this case? Justify your answer.

Short answer

a. No.

b. Condition of large counts is not met.

Step-by-step solution

Given Information

It is given that out of $76$passengers, $12$in first class and $64$in coach class.

Explaining 10% condition met in this case

It is not met as sample size of$10$is greater than$10\%$of population size of$76$.

Explaining large count condition

The sample size is $10$as $10$samples are taken for screening.

Neither$\mathrm{np}norn(1-p)$will be at least$10$.