how do you Calculate percentage when given standard deviation and mean

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score for that score. Change to a percentage.

If you mean percentile, the percentile is the percentage of scores below that score.

To calculate the percentage when given the standard deviation and mean, you need to know the distribution of data. Specifically, you need to know whether the distribution follows a normal distribution or another known distribution.

If you have a normal distribution, you can use the empirical rule or the z-score formula to calculate the percentage.

1. Using the Empirical Rule:
a. 68% of the data falls within one standard deviation of the mean.
b. 95% of the data falls within two standard deviations of the mean.
c. 99.7% of the data falls within three standard deviations of the mean.

2. Using the z-score formula:
a. Convert your value to a z-score using the formula: z = (x - mean) / standard deviation.
b. Look up the corresponding z-score in a standard normal distribution table (z-table) to find the percentage.

If your data does not follow a normal distribution and you know the specific distribution it follows, you may need to use different methods or formulas specific to that distribution.

However, if you are asked to calculate the percentage of data that falls within a certain range and you are given the standard deviation and mean, you can follow these steps:

1. Determine the range of values within which you want to calculate the percentage.
2. Calculate the z-scores for the lower and upper bounds of the range using the formula: z = (x - mean) / standard deviation.
3. Use a z-table to find the percentage corresponding to each z-score.
4. Subtract the lower percentage from the upper percentage to get the percentage of data within the desired range.

Remember that these methods assume a normal distribution or a known distribution. If you do not have this information, it may be challenging to calculate the percentage accurately.