Question 11, 7.2.17 HW Score: $71.11 \%, 10.67$ of 15 points Points: 0 of 1 Find the Z-scores that separate the middle $60 \%$ of the distribution from the area in the tails of the standard normal distribution. E Click the icon to view a table of areas under the normal curve. The Z-scores are $\square$. (Use a comma to separate answers as needed. Round to two decimal places as needed.) example Get more help - Clear all Check an
Solution
Step 1 ：The question is asking for the Z-scores that separate the middle 60% of the distribution from the area in the tails of the standard normal distribution. The standard normal distribution is symmetric around the mean, so the middle 60% of the distribution is equally divided on both sides of the mean. This means that 20% of the distribution is in each tail.
Step 2 ：We can use the Z-table to find the Z-scores that correspond to the cumulative probabilities of 20% and 80%.
Step 3 ：From the Z-table, we find that the lower Z-score is approximately -0.84 and the upper Z-score is approximately 0.84.
Step 4 ：The Z-scores that separate the middle 60% of the distribution from the area in the tails of the standard normal distribution are approximately -0.84 and 0.84.
Step 5 ：So, the final answer is \(\boxed{-0.84, 0.84}\).
