1. what are the mean and standard deviation for this distribution of weekly take-home pay amounts?
2. what percentage of the pay amounts lie within 1 standard deviations of the mean?
3. what percentage of the pay amounts lie within 2 standard deviations of the mean?
4. what percentage of the pay amounts lie within 3 standard deviations of the mean?
5. what is the range of the pay amounts?
What distribution?
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
http://en.wikipedia.org/wiki/File:The_Normal_Distribution.svg
To find the mean and standard deviation for the distribution of weekly take-home pay amounts, you'll need some data. If you have a dataset with the pay amounts, you can use that information to calculate the mean and standard deviation. Here's how:
1. Finding the Mean:
- Add up all the pay amounts in the dataset.
- Divide the sum by the total number of data points.
2. Finding the Standard Deviation:
- Calculate the difference between each of the pay amounts and the mean.
- Square each of these differences.
- Find the average of these squared differences by summing them up and dividing by the total number of data points.
- Take the square root of this average to get the standard deviation.
Once you have both the mean and standard deviation, you can answer the following questions:
2. To determine the percentage of pay amounts that lie within 1 standard deviation of the mean, you need to know the properties of a normal distribution. In a normal distribution, approximately 68% of the values fall within 1 standard deviation of the mean. So, approximately 68% of the pay amounts lie within this range.
3. To determine the percentage of pay amounts that lie within 2 standard deviations of the mean, again referring to a normal distribution, approximately 95% of the values fall within 2 standard deviations of the mean. Therefore, approximately 95% of the pay amounts lie within this range.
4. Similarly, approximately 99.7% of the values in a normal distribution fall within 3 standard deviations of the mean. Therefore, approximately 99.7% of the pay amounts lie within this range.
5. To find the range of the pay amounts, you need to know the minimum and maximum values in the dataset. Simply subtract the minimum value from the maximum value to get the range.
Remember, these answers are approximate as they assume a normal distribution. If your dataset follows a different distribution, the percentages may vary.