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: $\begin{array}{rcl}& & X~Exp(0.2)\end{array}$

What is the standard deviation?

Short answer

Standard Deviation of this Exponential Distribution is 5.

Step-by-step solution

Definition 

Standard deviation refers to the distribution of a statistical data compared to the mean value of the data.

Concept

As per provided information in the question, $\begin{array}{rcl}& & X~Exp(0.2)\end{array}$

Comparing with the standard formula of Exponential Distribution $\begin{array}{rcl}& & X~Exp\left(m\right)\end{array}$, it can be found out that;

$m=0.2$

Finding the Standard Deviation

Standard Deviation in case of Exponential Distribution is equal to the mean of the distribution.

Mean is the reciprocal of the decay variable $m$.

$\begin{array}{rcl}Mean\left(\mu \right)& =& \frac{1}{m}\\ & =& \frac{1}{0.2}\\ & =& 5\end{array}$

As Standard Deviation $(\begin{array}{rcl}& & \sigma \end{array}\begin{array}{rcl}& & )\end{array}$= Mean role="math" localid="1648203123884" $(\begin{array}{rcl}& & \mu \end{array}\begin{array}{rcl}& & )\end{array}$,

Therefore,

localid="1648203110749" role="math" $\begin{array}{rcl}\sigma & =& \mu \\ & =& 5\end{array}$

Thus, Standard Deviation is 5.