Question

Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: $X~Exp(0.2)$

Graph the distribution

Short answer

The graph related to the provided Exponential Distribution will be

Step-by-step solution

Concept of the given Exponential Distribution

As per given details, $X~Exp(0.2)$

Here, $m=0.2$

General form of Probability Density Function of Exponential Distribution,

$f\left(x\right)=m{e}^{-mx}$

Replacing $m$with $0.2$we get,

$f\left(x\right)=0.2e^{-0.2x}$

The above expression shows the probability density function of the problem.

Calculation of Mean

Mean of the given Expression is;

$\begin{array}{rcl}\mu & =& \frac{1}{m}\\ & =& \frac{1}{0.2}\\ & =& 5\end{array}$

Developing the Graph 

With the help of the gathered data, now development of the graph of the probability density function can be done. The maximum value that can be carried by $f\left(x\right)$which will be present on the localid="1648296710002">y-axisand at $x=0$will be;

$\begin{array}{rcl}f\left(0\right)& =& 0.2e^{-0.2\times 0}\\ & =& 0.2e^0\\ & =& 0.2\\ & =& m\end{array}$

Thus, it is proved that maximum value of $f\left(x\right)$will be equal to the value of $m$.

The graph can be developed as;