Question

Use the following information to answer the next four exercises: $X~N(54,8)$

Find the probability that$x<30$

Short answer

The value of $p(x<30)$is$0.0013$.

Step-by-step solution

Given Information

It is given that, $X~N(54,8)$

$\mu =54$

$\sigma =8$

Solution of the Problem

Now, the required probability can be calculated as below:

$P(x<30)=P\left(\frac{x-\mu }{\sigma }<\frac{30-\mu }{\sigma }\right)$

$=P\left(Z<\frac{30-54}{8}\right)$

$=P(Z<-3)$

$=0.0013\left\{\begin{array}{l}\text{From standard}\\ \text{normal table}\end{array}\right\}$