Question

Use the Cumulative Normal Distribution Table to find the z-scores that bound the middle 96% of the area under the standard.

normal curve. Enter the answers in ascending order. Round the answers to two decimal places.
The Z-scores for the given area are
and

Answer 1

The z-scores that bound the middle 96% of the area under the standard normal curve are approximately -2.05 and +2.05, looking up the z-table for the areas that leave 2% in the tails.

Step-by-step explanation:

To find the z-scores that bound the middle 96% of the area under the standard normal curve, we can use the Cumulative Normal Distribution Table. This involves finding the z-scores that leave 2% in the left tail and 2% in the right tail of the distribution.

Since the area to the left of the z-score represents the cumulative probability, we need to identify the z-score for 0.02 (2%) and subtract this from 1 to find the z-score for 0.98 (the remaining 98%).

Looking at a z-table, we can see that the z-score for an area of 0.02 to the left is approximately -2.05, and the z-score that corresponds to 0.98 is approximately +2.05. These are the z-scores that bound the middle 96% of the area under a standard normal curve.

Therefore, the z-scores for the given area are approximately -2.05 and +2.05, when rounded to two decimal places.