which z - values correspond to the middle 90% of the standard normal distribution? round your answers to the…

Answer:

$-1.645<z<1.645$

Explanation:

Step1: Determine the tail - area

The middle area is 90% or 0.9. So the total area in the two tails is $1 - 0.9=0.1$. Each tail has an area of $\frac{0.1}{2}=0.05$.

Step2: Use the z - table

We look for the z - value corresponding to an area of $0.05$ in the left - tail and an area of $1 - 0.05 = 0.95$ in the left - tail. Looking up in the standard normal (z) table, the z - value for an area of 0.05 is approximately $z=- 1.645$ and the z - value for an area of 0.95 is approximately $z = 1.645$.