Question

Bag check Thousands of travelers pass through the airport in Guadalajara,

Mexico, each day. Before leaving the airport, each passenger must go 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 traveler's luggage. Instead, they require each person to press a button. Either a red or a green bulb lights up. If the red light flashes, the passenger will be searched by customs agents. A green light means "go ahead." Customs agents claim that the light has probability $0.30$of showing red on any push of the button. Assume for now that this claim is true. Suppose we watch 20 passengers press the button. Let $R=$the number who get a red light. Here is a histogram of the probability distribution of $R$:

a. What probability distribution does R have? Justify your answer.

b. Describe the shape of the probability distribution.

Short answer

(a)All the binomial conditions are fulfilled here. Thus, it could be said that R follows the normal distribution.

(b) The distribution of R does not depart majorly from normality.

Step-by-step solution

Part (a) Step 1: Given Information

Given the graph,

Part (a) Step2: Simplification

Following requiremens are fulfilled by the random variable $R$.

1. Probability of success, that is, probability of getting red light on any press of the buttton ( $p$) which is equal to $0.30$is fixed.

2. Number of press are fixed.

3. Trials of getting red light are independent of each other.

4. There are two outcomes, that is getting red light and not getting red light.

All the binomial conditions are fullfilled here. Thus, it could be said that R follows the binomial distribution.

Part (b) Step 1: Given information

Given the graph is,

Part (b) Step 2: Simplification

The probability distribution shows that the shape of the histogram is roughly bell-shaped. As a result, the distribution of R does not deviate significantly from normality.