which z - values correspond to the middle 50% of the standard normal distribution? round your answers to the…

Explanation:

Step1: Determine the area in the tails

The middle area is 50% or 0.5. So the total area in the two - tails is (1 - 0.5=0.5). The area in each tail is (\frac{0.5}{2}=0.25).

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 (0.25). Looking up in the standard normal distribution table (or using a calculator with a normal - distribution function), if (P(Z < z_1)=0.25), then (z_1\approx - 0.674).

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

Since the standard normal distribution is symmetric about (z = 0), if the area to the left of (z_1) is (0.25), the area to the right of (z_2) is also (0.25) (where (z_2) is the positive (z) - value). So (P(Z<z_2)=0.75) (because (0.25 + 0.5=0.75)), and (z_2\approx0.674).

Answer:

(-0.674<z<0.674)