# Bag check Thousands of travelers pass through the airport

Chapter , Problem R7.5

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QUESTION:

Bag check Thousands of travelers pass through the airport in Guadalajara, Mexico, each day. Before leaving the airport, each passenger must pass through the Customs inspection area. Customs agents want to be sure that passengers do not bring illegal items into the country. But they do not have time to search every travelers luggage. Instead, they require each person to press a button. Either a red or a green bulb lights up. If the red light shows, the passenger will be searched by Customs agents. A green light means go ahead. Customs agents claim that the proportion of all travelers who will be stopped (red light) is 0.30, because the light has probability 0.30 of showing red on any push of the button. To test this claim, a concerned citizen watches a random sample of 100 travelers push the button. Only 20 get a red light. (a) Assume that the Customs agents claim is true. Find the probability that the proportion of travelers who get a red light is as small as or smaller than the result in this sample. Show your work. (b) Based on your results in (a), do you believe the Customs agents claim? Explain. s Find the mean and standard deviation of the sampling distribution of a sample mean x from an SRS of size n. s Calculate probabilities involving a sample mean x when the population distribution is Normal. s Explain how the shape of the sampling distribution of x is related to the shape of the population distribution.

QUESTION:

Bag check Thousands of travelers pass through the airport in Guadalajara, Mexico, each day. Before leaving the airport, each passenger must pass through the Customs inspection area. Customs agents want to be sure that passengers do not bring illegal items into the country. But they do not have time to search every travelers luggage. Instead, they require each person to press a button. Either a red or a green bulb lights up. If the red light shows, the passenger will be searched by Customs agents. A green light means go ahead. Customs agents claim that the proportion of all travelers who will be stopped (red light) is 0.30, because the light has probability 0.30 of showing red on any push of the button. To test this claim, a concerned citizen watches a random sample of 100 travelers push the button. Only 20 get a red light. (a) Assume that the Customs agents claim is true. Find the probability that the proportion of travelers who get a red light is as small as or smaller than the result in this sample. Show your work. (b) Based on your results in (a), do you believe the Customs agents claim? Explain. s Find the mean and standard deviation of the sampling distribution of a sample mean x from an SRS of size n. s Calculate probabilities involving a sample mean x when the population distribution is Normal. s Explain how the shape of the sampling distribution of x is related to the shape of the population distribution.

(a) We can calculate the probability of this sample result if the Customs agents' claim is true by using the binomial distribution. The probability of getting a red light is 0.30 and the n (sample size) is 100. Therefore, we can calculate the probability with the following equation: P(X ? 20) = P(X = 0) + P(X =