Question

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

Find $P(x>9)$.

Short answer

The value of the$P(x>9)$will be$0.25$.

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 value of localid="1647972154806" $P(x>9)$will be:

$P(x>9)=\text{base}\times \text{height}$

$=(12-9)\times \frac{1}{12}$

$=\frac{3}{12}$

$=0.25$