Question

Use the following information to answer the next eight exercises. A distribution is given as$X~U(0,12)$.

Find the ${40}^{th}$percentile

Short answer

The value of${40}^{\mathit{t}\mathit{h}}$percentile is$4.8$.

Step-by-step solution

Given information

A distribution is given as $X~U(0,12)$

Solution

The probability density function or height for variable $X$, which follows uniform distribution with parameter $(0,12)$, is shown below:

$f\left(x\right)=\frac{1}{12-0}$

$=\frac{1}{12}$

Thus the ${40}^{\text{th}}$percentile will be,

$P(x<k)=\text{base}\times \text{height}$

$0.40=(k-0)\left(\frac{1}{12}\right)$

$k=0.40\times 12$

$=4.8$