Question

what proportion of lsat scores will be outside the interval of 125 to 175?
step 2: compute the z - scores (z2 and z1). draw the distribution and shade the proportion.
z=\frac{x - mu}{sigma}
please enter the values into the z - score formula below.
z1 = choose your answer... - choose your answer... / choose your answer... = choose your answer...
z2 = choose your answer... - choose your answer... / choose your answer... = choose your answer...
what direction would we shade the distribution?
we are interested in the proportion choose your answer... of two z - scores which means we would shade choose your answer... the z - scores.

Explanation:

Step1: Identify values for z - score formula

Let $x_1 = 125$, $x_2=175$. We need population mean $\mu$ and standard - deviation $\sigma$. Assume $\mu$ and $\sigma$ are known. The z - score formula is $z=\frac{x - \mu}{\sigma}$.
For $z_1$: $z_1=\frac{125-\mu}{\sigma}$. Here, the first blank is $125$, the second blank is $\mu$, the third blank is $\sigma$.
For $z_2$: $z_2=\frac{175 - \mu}{\sigma}$. Here, the first blank is $175$, the second blank is $\mu$, the third blank is $\sigma$.

Step2: Determine shading direction

We are interested in the proportion outside of two z - scores. So we are interested in the proportion outside of two z - scores which means we would shade both tails of the standard normal distribution.

Answer:

$z_1$: First blank: $125$, Second blank: $\mu$, Third blank: $\sigma$
$z_2$: First blank: $175$, Second blank: $\mu$, Third blank: $\sigma$
Proportion: outside
Shading: both tails