For a standard normal curve, find the z-score that separates the bottom 90% from the top 10%.
To find the z-score that separates the bottom 90% from the top 10% in a standard normal curve, you can use the Z-table (also known as the standard normal distribution table) or a statistical calculator.
Here are the steps to find the z-score:
1. Start by understanding the symmetry of the standard normal distribution. Since it is symmetric around the mean (which is 0), the area above the mean is the same as the area below the mean. Therefore, the bottom 90% corresponds to an area of 0.9.
2. Subtract 0.9 from 1 to get the area above the top 10%. This gives us 0.1.
3. Identify the z-score associated with an area of 0.1 in the Z-table. The Z-table provides cumulative probability values for the standard normal distribution. Locate the closest value to 0.1 in the table. In this case, it is approximately 1.28.
4. However, since we want the value that separates the bottom 90% from the top 10%, we need to consider the left-tail area. The z-score corresponding to a cumulative probability of 0.1 in the left tail is -1.28 (opposite sign of 1.28).
Therefore, the z-score that separates the bottom 90% from the top 10% in a standard normal curve is approximately -1.28.
To find the z-score that separates the bottom 90% from the top 10% of a standard normal curve, you can use the inverse normal distribution function.
Step 1: Subtract the desired percentage (10%) from 1 to get the area of the bottom portion.
1 - 0.10 = 0.90
Step 2: Divide the remaining area by 2 to account for both tails of the distribution.
0.90 / 2 = 0.45
Step 3: Look up the value of 0.45 in the standard normal distribution table or use a calculator and find its corresponding z-score.
The z-score that corresponds to 0.45 is approximately 1.28.
Therefore, the z-score that separates the bottom 90% from the top 10% of a standard normal curve is approximately 1.28.
In the back of your statistics text, there is a table labeled something like "areas under the normal distribution." Look for the portion values for the larger or smaller portion to get your Z score.
I hope this helps.