Chapter 11.4, Problem 1CYU

To determine

Determine whether each experiment is a binomial experiment or can be reduced to a binomial experiment.

Answer to Problem 1CYU

  $\boxed{\text{NOT a binomial experiment}}$

Explanation of Solution

Given information:

A study finds that $58\%$ of people have pets. You ask $100$ people how many pets they have. Determine whether each experiment is a binomial experiment or can be reduced to a binomial experiment. If so, describe a trial, determine the random variable, and state $n$ , $p$ , and $q$ .

Calculation:

Examine an experiment that a person asks $100$ people how many pets them they have.

A bionomail experiment is an experiment with $n$ number of indipendent trials and each trial has only two possible outcomes, success or failure. In a trial, the probablity of success is $p$ and that of failure is:

  $q=1-p$

The above experiment has as many outcomes as the number of pets a person can have in a single trial. So, the number of possible outcomes in a trial is not two.

Hence, the experiment of a person asking $100$ people hoe many pets that each of them have is $\boxed{\text{NOT a binomial experiment}}$