Question

Suppose $X~N(4,2)$. What value of $x$ is two standard deviations to the right of the mean?

Short answer

The value of$x$is two standard deviations to the right of the mean is$8.$

Step-by-step solution

Given Information 

Given in the question that, $X~N(4,2)$.

We have to find what value of $x$is two standard deviations to the right of the mean?

Explanation 

Let's consider $X~N(4,2)$.

Where,

$\mu =4$

$\sigma =2$

From the information given in the question, we observe that the $z$value is $2$.

Let's compute the value of $z$score:

$z=\frac{x-\mu }{\sigma }$

Now, place the provided value in the above equation.

Therefore,

$2=\frac{x-4}{2}$

$x-4=2\times 2$

$x=4+4$

$x=8$