Chapter 11.4, Problem 2CYU

To determine

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

Answer to Problem 2CYU

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

Explanation of Solution

Given information:

You roll a die $15$ times and find the sum of all the rolls.

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:

Study an experiment that a person roll a die $15$ times and find the sum of all the rolls.

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:

  $q=1-p$

In the above experiment, there are $6$ outcomes in a single roll. So, when the outcomes of the $15$ rolls are added, there are not only $2$ outcomes. So, the number of possible outcomes in atrial is not two.

Hence, the experiment of a person rolling a die $15$ times and finding the sum of all the rolls is $\boxed{\text{NOT a binomial experiment}}$