which z - values correspond to the middle 30% of the standard normal distribution? round your answers to the…

Explanation:

Step1: Determine the area in the tails

The middle area is 30% or 0.3. So the total area in the two - tails is (1 - 0.3=0.7). The area in each tail is (\frac{0.7}{2}=0.35).

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 (0.35). 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 (0.35) is approximately (z_1=- 0.385).

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 (0.35) to the right of the middle 30%) is (z_2 = 0.385).

Answer:

(-0.385<z<0.385)