Find the z-scores that separate the middle 40% of the distribution from the area in the tails of the standard normal distribution.
You can play around with Z table stuff at
davidmlane.com/hyperstat/z_table.html
To find the z-scores that separate the middle 40% of the distribution from the area in the tails of the standard normal distribution, we need to find the z-scores that correspond to the cumulative probabilities that divide the distribution in the following way:
The middle 40% of the distribution corresponds to 50% + 40%/2 = 70% on one side, and 50% - 40%/2 = 30% on the other side.
1. Start by finding the z-score that corresponds to the cumulative probability of 70% using the standard normal distribution table or a calculator. The value corresponding to 70% is 0.5244.
2. Next, find the z-score that corresponds to the cumulative probability of 30%. Since the standard normal distribution is symmetric, this z-score will be the negative of the z-score found in step 1. Thus, the value corresponding to 30% is -0.5244.
So, the z-scores that separate the middle 40% of the distribution from the areas in the tails of the standard normal distribution are approximately -0.5244 and 0.5244.