weekly take home pay for those 20 graduate teaching assistants from university z:

500.75, 217.43, 488.25, 405.78
485.46, 495.48, 370.75, 435.40
479.65, 482.56, 470.28, 489.90
382.50, 500.75, 465.32, 481.25
506.43, 225.50, 504.38, 179.25

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 isthe range of the pay amounts?

To answer these questions, we need to calculate the mean, standard deviation, and range of the pay amounts. Here's how you can do that:

1. To find the mean, add up all the pay amounts and divide the sum by the total number of values. In this case, we have 20 pay amounts. So, sum all the pay amounts and divide by 20 to get the mean.

2. To calculate the standard deviation, the first step is to find the variance. Variance measures how spread out the values are from the mean. To find the variance, subtract the mean from each pay amount, square the result, sum up all the squares, and divide by the total number of values. Once you have the variance, you can calculate the standard deviation by taking the square root of the variance.

3. To determine the percentage of pay amounts within 1 standard deviation of the mean, we need to count the number of pay amounts that fall within one standard deviation above and below the mean. Then, divide that count by the total number of values and multiply by 100 to get the percentage.

4. Similarly, to find the percentage of pay amounts within 2 standard deviations of the mean, count the number of pay amounts that fall within two standard deviations above and below the mean. Divide that count by the total number of values and multiply by 100.

5. To calculate the percentage of pay amounts within 3 standard deviations of the mean, count the number of pay amounts that fall within three standard deviations above and below the mean. Divide that count by the total number of values and multiply by 100.

6. Finally, to determine the range of the pay amounts, subtract the lowest value from the highest value.

By following these steps, you should be able to answer the questions about the mean, standard deviation, range, and percentages of the pay amounts.