3. a) What is the 99th percentile of the Standard Normal (z) DIstribution?
b) Between what two values is the middle 99% of the Standard Normal (z) DIstribution?
To find the 99th percentile of the Standard Normal (z) Distribution, we can use a z-table or a statistical calculator.
a) Using a z-table:
1. Look for the z-value closest to 0.99 in the z-table. Typically, the table provides the area to the left of the z-value.
2. Locate the corresponding z-value in the table.
For example, if the closest z-value is 2.33, it means that the area under the curve to the left of 2.33 is approximately 0.9900. Hence, the 99th percentile of the Standard Normal Distribution is 2.33.
b) To determine the range between which the middle 99% falls, we subtract the value at the 99th percentile from the value at the 1st percentile.
1st percentile = -2.33 (as the Standard Normal Distribution is symmetric around 0)
99th percentile = 2.33
So, the range is from -2.33 to 2.33.