which z - values correspond to the middle 80% of the standard normal distribution? round your answers to the…

Answer:

$- 1.282<z<1.282$

Explanation:

Step1: Determine the tail - areas

Since the middle area is 80% or 0.8, the total area in the two tails is $1 - 0.8=0.2$. So the area in each tail is $\frac{0.2}{2}=0.1$.

Step2: Use the z - table

We want to find the z - value such that the area to the left of it is $0.1$ and $0.9$ (because $0.1$ is in the left - tail and $0.8 + 0.1=0.9$ for the right - hand side of the middle 80% region). Looking up in the standard normal (z -) table, the z - value corresponding to an area of 0.1 is approximately $z=-1.282$ and the z - value corresponding to an area of 0.9 is approximately $z = 1.282$.