Question

Use the following information to answer the next seven exercises. A distribution is given as $X~Exp(0.75)$. Find the 30th percentile

Short answer

The value of 70 percentile is 0.4756

Step-by-step solution

Function of commutative distribution  

As the rule of commutative distribution

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

It has been said

$X~Exp(0.75)$

$m=0.75$

Formula of commutative distribution  

In order to 30 percentile calculation

$$\begin{gathered} P(x<k)=1-e^{-0.75x} \\ 0.30=1-e^{-0.75x} \\ {e}^{-0.75x}=0.70 \end{gathered}$$

Equation of commutative distribution  

Applying logarithm in both sides

$$\begin{gathered} \ln e^{0.75k}=\ln 0.70 \\ k=0.4756 \end{gathered}$$

The value of 70 percentile is 0.4756