Chapter 11.4, Problem 3GP

To determine

What is the probability that $5$ calls result in a sale?

Answer to Problem 3GP

  $\boxed{\text{H }\left(\text{10}\text{.3\%}\right)}$ is correct option.

Explanation of Solution

Given information:

At Jenny’s telemarketing job, $15\%$ of the calls that she makes to potential customers result in a sale. She makes $20$ calls in a given hour. What is the probability that $5$ calls result in a sale?

  $\text{F 6}\text{.7\%}$

  $\text{G 8}\text{.3\%}$

  $\text{H 10}\text{.3\%}$

  $\text{J 11}\text{.9\%}$

Calculation:

Consider a survey in which $15\%$ of the calls that she makes to potential customers result in a that she makes to potential customers result in a sale.

The probability of successes in $n$ trials of a binomial experiment is,

  $P(k)=C{}_k{(p)}^k{(q)}^{n-k}$

Here, $p$ represents the probability of success and $q$ represents the probability of failure which is equal to,

  $q=1-p$

Since, $15\%$ of the calls that she makes to potential customers result in a sale, so,

  $p=15\%$

  $=0.15$

The probability of failure is,

  $q=1-p$

  $\begin{array}{l}=1-0.15\\ =0.85\end{array}$

Substitute $p=0.15,q=0.85,k=3,n=20$ in the above formula to find the probability that $5$ out of $20$ calls results in a sale in a given hour.

  $P(5)=C{}_5{(0.15)}^5{(0.75)}^{20-5}$

  $\begin{array}{l}=15504(0.0000759375)(0.873542191)\\ =0.1028\\ =10.28\%\\ \approx 10.3\%\end{array}$

The probability that $5$ out of $20$ calls results in a sale in a given hour is $\boxed{10.3\%}$ .

Hence, the correct option is $\boxed{\text{H 10}\text{.3\%}}$