Chapter 11.4, Problem 3CYU

To determine

Determine the random variable, and state $n$ , $p$ , and $q$ .

Answer to Problem 3CYU

  $n=\boxed{30}$ , $p=\boxed{0.72}$ and $q=\boxed{0.28}$ .

Explanation of Solution

Given information:

A poll found that $72\%$ of students plan on going to the homecoming dance. You ask $30$ students if they are going to the homecoming dance.

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:

consider an experiment a person roll asks $30$ students if they are going to the homecoming dance.

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 only two possible outcomes in trial, that is, a student can say either yes or no to the question. hence, the experiment of a person asking $30$ students if they want to go the homecoming dance is $\boxed{\text{a binomial experiment} }$ .

Since there are $30$ students, the number of trials that is $n$ is 30. Since an opinion poll in the school found that $72\%$ of the students want to go the homecoming dance, the probability of success, $p$ is,

  $\begin{array}{l}p=72\%\\ =\frac{72}{100}\\ =0.72\end{array}$

The probability of failure, $q$ is,

  $\begin{array}{l}q=1-p\\ =1-0.72\\ =0.28\end{array}$

Hence, the values are $n=\boxed{30}$ , $p=\boxed{0.72}$ and $q=\boxed{0.28}$ .