which z - values correspond to the middle 20% of the standard normal distribution? round your answers to the…

Explanation:

Step1: Determine the area in the tails

The middle area is 20% or 0.2. So the total area in the two - tails is (1 - 0.2=0.8). The area in each tail is (\frac{0.8}{2}=0.4).

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 (0.4). Looking up in the standard normal distribution table (or using a calculator with a normal - distribution function), the (z) - value corresponding to an area of (0.4) is approximately (z_1=- 0.253).

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

Since the standard normal distribution is symmetric about (z = 0), the (z) - value for the right - hand tail (with area (0.4) to the right of it) is (z_2 = 0.253).

Answer:

(-0.253<z<0.253)