If I don't know the mean and the standard deviation how can I find the area of z-score -0.75
To find the area corresponding to a specific z-score without knowledge of the mean and standard deviation, we need to refer to a standard normal distribution table.
A standard normal distribution table (also known as a z-table) provides the cumulative probability, or area, to the left of a given z-score. Each entry in the table represents the proportion of the standard normal distribution that falls to the left of that specific z-score.
Here's how you can find the area corresponding to a z-score of -0.75 using a standard normal distribution table:
1. Look for the value closest to -0.75 in the z-table.
2. The z-table is usually organized in two sections: the left section represents the tenths digit of the z-score, and the top section represents the hundredths digit. Find the intersection of the row and column that corresponds to the closest z-score value.
3. The value in the table at the intersection represents the area to the left of the z-score. Since we are interested in the area to the right of the z-score, subtract this value from 1 to obtain the area to the right.
For example, if the value in the table is 0.2266, subtract it from 1: 1 - 0.2266 = 0.7734.
Therefore, the area to the right of a z-score of -0.75 is approximately 0.7734.
Keep in mind that this method assumes that you are dealing with a standard normal distribution (mean of 0 and standard deviation of 1). If you have a different mean and standard deviation, you would need to use additional calculations to standardize the z-score before utilizing the z-table.