If I don't know the mean and the standard deviation how can I find the area of z-score -0.75
I thought I had given you the answer.
finding the z-score results in a mean of 0 and a standard deviation of 1
so in the link I gave you ....
http://davidmlane.com/hyperstat/z_table.html
enter 0 for the mean
1 for the sd
click on "below" and enter -.75
click on "calculate" to get .2266
To find the area of a specific z-score without knowing the mean and standard deviation, you will need to refer to a standard normal distribution table or use statistical software.
Here's how you can find the area of the z-score -0.75 using a standard normal distribution table:
1. Look for the absolute value of the z-score, which is 0.75, in the body of the table.
2. Find the corresponding row and column that intersect with this value. For the sake of simplicity, assume you find the value located at the intersection of row 0.7 and column 0.05 (these rows and columns are typically provided in the table).
3. Take note of the value in the table, which represents the cumulative probability associated with the z-score of -0.75. Let's say it is 0.2266.
4. Since the standard normal distribution is symmetric, the area to the left of -0.75 is equal to the absolute value of the area to the right of 0.75. Subtract the value obtained in step 3 from 0.5 (which represents the total area under the curve) to get the area to the left of -0.75: 0.5 - 0.2266 = 0.2734.
Therefore, the area to the left of the z-score -0.75 is approximately 0.2734.
Note: If you have access to statistical software such as Excel, you can also use the NORM.S.DIST function or other relevant functions to find the area directly without referring to a table manually.