Question

Use the following information to answer the next four exercises. Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about $4\%.$ Of the next $25$patients calling in claiming to have the flu, we are interested in how many actually have the flu.
Define the random variable and list its possible values.

Short answer

X is a random variable that represents the number of people that are infected with the virus. $x=0,1,2,3,4,5,6,7,........,25$ is a possible value.

Step-by-step solution

Given information

The number of people being polled is $25.$

The probability of being chosen and having flu is $0.04.$

Explanation

We assume X to be a random variable that represents the number of people who are in fact infected with the virus. In this question, we'll take a sample of $25$patients, withX being the number of persons out of $25$who are genuinely sick with the flu.

The random variableX can take on any of the following values: $0,1,2,3,4,5,6,7,........25.$This is because we're taking a sample of$25$people, and X may be$0$ if no one has the virus, or it could be $25$ if everyone has the illness.