Question

Find the $60th$percentile.

Short answer

The value of ${60}^{\text{th}}$the Percentile is 50.0264

Step-by-step solution

Given Information

Given that,

$X~N(54,8)$

Where,

$\mu =54$

$\sigma =8$

Explanation

Now,${60}^{\text{th}}$percentile can be calculated as below:

$P(x<k)=P\left(\frac{x-\mu }{\sigma }<\frac{k-\mu }{\sigma }\right)$

$0.6=P\left(Z<\frac{k-54}{8}\right)$

$\frac{k-54}{8}=0.2533\left\{\begin{array}{l}\text{From standard}\\ \text{normal table}\end{array}\right\}$

$k-54=0.2533\times 8$

$k=2.0264+54$

$k=56.0264$