Answer:
To sketch the Normal Curve representing the data with a mean of 21 years and a standard deviation of 2.1 years, you can follow these steps:
1. Determine the key points:
- The mean (average) age is 21 years.
- The standard deviation is 2.1 years.
- You want to label the mean and three standard deviations above and below the mean.
2. Calculate the values for each standard deviation:
- One standard deviation above the mean: Mean + (1 * Standard Deviation) = 21 + (1 * 2.1) = 23.1 years.
- Two standard deviations above the mean: Mean + (2 * Standard Deviation) = 21 + (2 * 2.1) = 25.2 years.
- Three standard deviations above the mean: Mean + (3 * Standard Deviation) = 21 + (3 * 2.1) = 27.3 years.
- One standard deviation below the mean: Mean - (1 * Standard Deviation) = 21 - (1 * 2.1) = 18.9 years.
- Two standard deviations below the mean: Mean - (2 * Standard Deviation) = 21 - (2 * 2.1) = 16.8 years.
- Three standard deviations below the mean: Mean - (3 * Standard Deviation) = 21 - (3 * 2.1) = 14.7 years.
3. Now, you can sketch the Normal Curve on a piece of paper or using a graphing tool, labeling the mean and the points calculated in step 2 on the x-axis. Here's a simple text representation of the curve:
```
^
|
| * (27.3 years)
|
|
|
| * (25.2 years)
|
|
|
| * (23.1 years)
|
|
|
| * (21 years, Mean)
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|
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| * (18.9 years)
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|
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|* (16.8 years)
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|
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|* (14.7 years)
+--------------------------------->
14.7 16.8 18.9 21 23.1 25.2 27.3
```
This sketch visually represents the Normal Curve for the average age of WCU students, with the mean and three standard deviations labeled. The curve is centered at the mean of 21 years and spreads out symmetrically with the standard deviation determining the spread.
Explanation: