Question

55.

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

modelled by the following distribution:$X~Exp(0.2)$

Find the 70th percentile.

Short answer

The answer of 70th percentile is$6.02$

Step-by-step solution

Rule of random variables 

The rule of commutative is distribution

$P(X<x)$= $(-)(e^{-mx}-1)$

Here m =$0.2$[m is mean value]

Step  : Formula of  random theory 

For 70% calculation

$P(x<k)$= $1-e^{-0.2k}$

role="math" localid="1648210393381" $0.70=1-e^{-0.2k}$

$e^{-0.2k}=1-0.70$

$e^{-0.2k}=0.30$

Applying logarithm in both side

localid="1648210516786" $$\begin{gathered} \ln \left(e^{-0.2k}\right)=\ln (0.30) \\ -0.2k=-1.2040 \\ k=\frac{-1.2040}{-0.2k} \\ k=6.02 \end{gathered}$$

The answer of 70th percentile is 6.02