Question

passengers of travelers pass through the airport in guadalajara, mexico, each day. mexican customs agents want to be sure that known to pass a button. either a red or a green bulb lights up. if red, the passenger will be searched by customs agents. green 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.
(a) find the probability that at most 3 people out of 20 would get a red light if the agents’ claim is true.
(0.0121
(round to 4 decimal places. leave your answer in decimal form.)
(b) suppose that only 2 of the 20 passengers get a red light after pressing the button. does this give convincing evidence that the customs agents’ claimed value of p = 0.3 is too high? explain your reasoning.

Explanation:

Answer:

0.0121
No, because the probability of at most 3 people getting a red light is very low (0.0121), which is less than 0.05. So it is more likely that the agents' claimed value of \( p = 0.3 \) is too high.