Chapter 11.4, Problem 7PPS

To determine

Determine whether each experiment is a binomial experiment.

Answer to Problem 7PPS

  $\boxed{\text{a binomial experiment}}$

  $n=$

  $\boxed{\text{number of days in a month} }$

  $,p=\boxed{0.35}$

  $\text{and}$

  $q=\boxed{0.65}$

Explanation of Solution

Given information:

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 $q$ .

There is a $35\%$ chance that it rains each day in a given month. You record the number of days that it rains for that month.

Calculation:

Consider an experiment:

A person records the number of days it rains for a month.

A binomial experiment is an experiment with $n$ number of independent trials and each trial has only two possible outcomes. Success or failure. In a trial, the probability of success is $p$ and that of failure is,

  $q=1-p$

In the above experiment, there are only two possible outcomes in a trial, that is, it rains on a day or it does not rain.

Hence, the experiment of a person recording the number of days it rains for a month is $\boxed{\text{a binomial experiment}}$ .

The number of days will be the number of trials, $n.$

As there is chance that it rains on a day, the probability of success, $p$ , is

  $\begin{array}{l}p=35\%\\ =\begin{array}{c}35\\ 100\end{array}\\ =0.35\end{array}$

The probability of failure, $q$ ,is

  $\begin{array}{l}q=1-p\\ =1-0.35\\ =0.65\end{array}$

Hence, the values are $n=$

  $\boxed{\text{number of days in a month} }$

  $,p=\boxed{0.35}$

  $\text{and}$

  $q=\boxed{0.65}$ .