what is the percentage of the area under the curve is above the mean of the normal curve

Since mean, mode and median have the same value in a normal distribution, 50%.

To find the percentage of the area under the curve that is above the mean of the normal curve, you will need to use a standard normal distribution table or a calculator with a normal distribution function.

Here is how you can determine the percentage step-by-step:

1. Calculate the z-score: The z-score measures how many standard deviations the mean is away from a specific value on the normal distribution curve. To calculate the z-score for the mean, you can use the formula:

z = (x - μ) / σ

Where:
- x is the value you want to compare to the mean
- μ is the mean of the normal distribution
- σ is the standard deviation of the normal distribution

In this case, since you want to find the percentage above the mean, x would be the mean.

2. Look up the z-score in a standard normal distribution table: The standard normal distribution table provides the cumulative probabilities for various z-scores. It tells you the percentage of the area under the curve to the left of a given z-score.

The z-score of the mean is always 0. So, you can look up the z-score of 0 in the table, which will give you the percentage of the area to the left of the mean.

3. Calculate the percentage above the mean: Once you have the percentage to the left of the mean from the z-score table, subtract that value from 100% to find the percentage above the mean.

Percentage above the mean = 100% - Percentage to the left of the mean

For example, if the z-score table tells you that the percentage to the left of the mean is 40%, then the percentage above the mean would be 100% - 40% = 60%.

By following these steps and using a z-score table or calculator, you can determine the percentage of the area under the curve that is above the mean of the normal curve.