<\/span><\/h2>\n\nTo find the Z critical value from a given percentile, follow these steps:<\/p>\n
Step 1:<\/b> Identify the percentile you want to find the Z critical value for. Let’s say it is 80%.<\/p>\n
Step 2:<\/b> Convert the percentile to a decimal format. In this case, 80% becomes 0.80.<\/p>\n
Step 3:<\/b> Determine the area to the left of the desired percentile. Since the Z distribution is symmetric, we will always look for the left-hand side area. Therefore, the area to the left of 0.80 is 0.8000.<\/p>\n
Step 4:<\/b> Use a Z table or statistical software to find the Z score associated with the area from step 3. Locate the area in the body of the table and read the corresponding Z score. For our example, the Z score is approximately 0.84.<\/p>\n
Step 5:<\/b> The Z critical value is the Z score found in step 4, whether positive or negative. In this case, the Z critical value is \u00b10.84.<\/p>\n
Example:<\/b> To find the Z critical value for the 90th percentile, convert 90% to a decimal (0.90), find the area to the left (0.9000), use the Z table to find the Z score (approximately 1.28), and finally, the Z critical value is \u00b11.28.<\/p>\n