How to Construct the Normal Distribution Curve Given the Mean and Standard Deviation

Understanding Normal Distribution Curves

Introduction to Normal Distribution

• The normal distribution curve, often referred to as the bell curve, has a shape resembling a bell. The center of this curve represents the mean, which divides it into two symmetric parts: left and right.

Key Features of the Normal Curve

• The left and right sides of the normal curve are symmetric; if folded at the mean, both sides align perfectly. This symmetry is crucial for understanding data distribution.

• The ends of the normal curve taper off towards horizontal lines known as asymptotes; they approach but never touch these lines, indicating that extreme values become less likely but are still possible.

• The normal curve is segmented by standard deviations from the mean, illustrating how spread out or concentrated data points are around the average value. One standard deviation below and above can be visualized on this graph.

Constructing a Normal Distribution Curve

Example 1: Mean = 48, Standard Deviation = 13

• To sketch a normal distribution with a mean of 48:

• Label the center (mean) as 48.

• Calculate one standard deviation below: 48 - 13 = 35.

• Two standard deviations below: 35 - 13 = 22.

• One standard deviation above: 48 + 13 = 61.

• Two standard deviations above: 61 + 13 = 74.

Answering Questions Based on Calculations

• Identify one standard deviation below the mean (35) and two standard deviations above (74). Extend further to find three standard deviations below by calculating 22 - 13 = 9. Thus, three standard deviations below is labeled as such on your graph.

Second Example: First Graders' Heights

Given Data: Mean = 37 inches, Standard Deviation = 2 inches

• Create another bell curve with:

• Center labeled as mean (37).

• One standard deviation below calculated as 37 -2 =35 and then 35 -2 =33.

• One standard deviation above calculated as 37 +2 =39 and then 39 +2 =41.