Question

Suppose X ~ N(4, 2). What value of x is 1.5 standard deviations to the left of the mean?

Short answer

The value of x is 1

Step-by-step solution

Given Information

Given that$X~N(4,2)$

We have to find the value of x 1.5 standard deviations to the left of the mean

Explanation

The value of $z$-score can be calculated as below:

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

Put the provided values in the above expression. Then,

$-1.5=\frac{x-4}{2}$

$x-4=-1.5\times 2$

$x=-3+4$

$x=1$