which z - values correspond to the middle 40% of the standard normal distribution? round your answers to the…

Explanation:

Step1: Determine the area in the tails

The middle area is 40% or 0.4. The total area under the standard - normal curve is 1. So the area in the two tails combined is (1 - 0.4=0.6). The area in each tail is (\frac{0.6}{2}=0.3).

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 (0.3). Using a standard normal table (or z - table) or a calculator with a normal - distribution function (e.g., invNorm on a TI - 84 Plus: invNorm(0.3,0,1)), we find that (z_1\approx - 0.524).

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 such that the area to the left of it is (0.3 + 0.4=0.7) (or the area to the right is 0.3) is (z_2\approx0.524) (using invNorm(0.7,0,1) on a calculator or the z - table).

Answer:

(-0.524<z<0.524)