Chapter SH, Problem 11.10EP

To determine

To create a histogram using graphing calculator and then describe the distribution of the shape.

Answer to Problem 11.10EP

  $0.0836$

Explanation of Solution

Given:

A survey which states that $34\%$ of homeowners own a dog.

Calculation:

The probability that a randomly selected homeowner owns a dog is as follow:

  $p=0.34$

The value of q will be as follows:

  $\begin{array}{l}q=1-0.34\\ q=0.66\end{array}$

Use the Binomial Probability Formula as follow:

The probability of X successes in independent trials is given below:

  $P(x)=C(n,x)p^x{q}^{n-x}$ ”

So, the probability that out of $10$ randomly selected homeowners, more than $5$ own a dog is calculated below:

  $\begin{array}{l}P(X>5)=C(10,6)p^6{q}^{10-6}+C(10,7)p^7{q}^{10-7}+\mathrm{..........}+C(10,10)p^{10}{q}^{10-10}\\ P(X>5)=0.0836\end{array}$

Hence, the required probability is $0.0836$ .