Question

Suppose $x^{~}N(8,9)$. What value of $x$is $0.67$standard deviations to the left of the mean?

Short answer

The value of$x$is$1.97$

Step-by-step solution

Given Information

Given in the question that, $X~N(8,9)$

We have to find the value of $x$is $0.67$standard deviations to the left of the mean.

Explanation 

According to the information, the value of $z$is $-0.67$

Here, localid="1649394314342" $X^{~}N(8,9)$

Where, $\mu =8$

$\sigma =9$

We can compute the value of $z$score as follow:

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

Place the given value in the above equation.

$-0.67=\frac{x-8}{9}$

$x-8=-0.67\times 9$

$x=-6.03+8$

$x=1.97$