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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 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 Normal condition met in this case? Justify your answer.

Short Answer

Expert verified

a. No, the 10%condition is not met in this case.

b. No, the Normal condition is not met in this case.

Step by step solution

01

Part (a) Step 1: Given Information 

Number of passengers in flight=76

First-class passengers =12in first class

Coach class passengers =64

Passengers for SRS screening=10

02

Part (a) Step 2: Explanation 

Based on the 76-person population, here the sample size of 10 is greater than 10%of the 76 -person population so the10%condition is not met.

03

Part (b) Step 1: Given Information

Number of passengers in flight=76

First-class passengers =12in first class

Coach class passengers=64

Passengers for SRS screening =10

04

Part (b) Step 2: Explanation 

Given for the population:

x=12

n=76

Based on the sample size divided by the number of successes, the population proportion is:

localid="1650014761501" p=xn=1276

Sample given:

n=10

As long as npand n(1-p)are both at least 10, the condition is met.

localid="1650014767325" np=10×1276≈1.58

localid="1650014773670" n(1−p)=10×1−1276≈8.42

Neither of them exceeds 10, so the Normal condition has not been met.

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