When labeling a normal distribution curve with a given mean and standard deviation, you'll follow these steps:
1. **Mark the Mean:** First, you identify the center of your normal distribution curve. This is the mean of the distribution. In the case of IQ scores, where the mean is 100 points, you would place a tick mark labeled '100' at the center of the x-axis on your graph.
2. **Mark the Standard Deviations:** The next step is to mark off points on the x-axis that are equidistant from the mean, at intervals of one standard deviation. Since the standard deviation for IQ scores is given as 15 points, you would mark points on the x-axis that are 15 points away from the mean in both directions (to the left and to the right).
3. **Create the Tick Marks:** You'll create a set of tick marks extending to at least three standard deviations on either side of the mean (but up to four or more can be used for a more detailed graph). For the IQ score distribution, you would:
- Subtract 15 points from 100 to find the first tick mark to the left of the mean: 100 - 15 = 85.
- Add 15 points to 100 to find the first tick mark to the right of the mean: 100 + 15 = 115.
- Continue this process, subtracting and adding multiples of 15, to create additional tick marks.
Here are the tick marks you would label:
- **4 Standard Deviations below the Mean:** 100 - 4(15) = 40
- **3 Standard Deviations below the Mean:** 100 - 3(15) = 55
- **2 Standard Deviations below the Mean:** 100 - 2(15) = 70
- **1 Standard Deviation below the Mean:** 100 - 1(15) = 85
- **Mean (0 Standard Deviations):** 100
- **1 Standard Deviation above the Mean:** 100 + 1(15) = 115
- **2 Standard Deviations above the Mean:** 100 + 2(15) = 130
- **3 Standard Deviations above the Mean:** 100 + 3(15) = 145
- **4 Standard Deviations above the Mean:** 100 + 4(15) = 160
Label these values respectively on the x-axis from left to right. Your curve should now show a normal distribution with the mean marked at 100 and the standard deviations marked at 15-point intervals away from the mean.
