Chapter 6.3, Problem 97E

a.

To determine

To find: The probability that more than 12 calls does not get completed.

Answer to Problem 97E

The probability is 0.8531.

Explanation of Solution

Given:

Probability of success ( p ) = 9% = 0.09

Number of trials ( n ) = 15

Formula used:

The formula to compute the mean and standard deviation are:

  $\begin{array}{l}\text{Mean}\left(\mu \right)=n\times p\\ \text{Standard deviation}\left(\sigma \right)=\sqrt{n\times p\times \left(1-p\right)}\end{array}$

Calculation:

Consider, X be the random that represents the number of calls that help in completing survey follows the binomial distribution.

If more than 12 calls does not get completed it means fewer than 3 calls are completed.

The probability can be calculated as:

  $\begin{array}{c}P\left(X<3\right)=P\left(X=0\right)+P\left(X=1\right)+P\left(X=2\right)\\ ={\displaystyle \sum _{r=0}^2{}^{15}{C}_r\times {\left(0.09\right)}^r\times {\left(1-0.09\right)}^{15-r}}\\ =0.8531\end{array}$

Thus, the required probability is 0.8531.

b.

To determine

To find: The mean of X and interpret it.

Answer to Problem 97E

The mean is 1.35.

Explanation of Solution

The mean of X can be calculated as:

  $\begin{array}{c}{\mu }_X=n\times p\\ =15\left(0.09\right)\\ =1.35\end{array}$

Thus, the mean is 1.35

Interpretation:

The computed value of mean shows that on an average out of 15 calls , 1.35 will be completed.

c.

To determine

To find: The standard deviation of X and interpret it.

Answer to Problem 97E

The standard deviation is 1.35

Explanation of Solution

The standard deviation of X can be calculated as:

  $\begin{array}{c}{\sigma }_X=\sqrt{n\times p\times \left(1-p\right)}\\ =\sqrt{15\left(0.09\right)\left(1-0.09\right)}\\ =1.1084\end{array}$

Interpretation:

The total number of calls that get completed will vary by 1.1084 calls in comparison of mean of 1.35 calls..