which z - values correspond to the middle 60% of the standard normal distribution? round your answers to the…

Explanation:

Step1: Determine the area in the tails

Since the middle area is 60% or 0.6, the total area in the two - tails is $1 - 0.6=0.4$. So the area in each tail is $\frac{0.4}{2}=0.2$.

Step2: Find the z - value for the left - hand tail

We want to find the $z$-value such that the area to the left of it is $0.2$. Using a standard normal distribution table (or a calculator with a normal - distribution function), if $P(Z < z_1)=0.2$, then $z_1\approx - 0.842$.

Step3: Find the z - value for the right - hand tail

The area to the left of the right - hand $z$-value is $0.2 + 0.6=0.8$. Using the standard normal distribution table (or a calculator), if $P(Z < z_2)=0.8$, then $z_2\approx0.842$.

Answer:

$-0.842<z<0.842$