Question

Sketch a curve showing a distribution that is symmetric and bell-shaped and has approximately the given mean and standard deviation. In each case, draw the curve on a horizontal axis with scale 0 to 10. Mean 5 and standard deviation 2.

Short answer

The curve should be drawn as a bell shape centered around the mean of 5, with inflection points at 3 and 7, representing one standard deviation to each side of the mean.

Step-by-step solution

- Set up Your Axes

First, draw a horizontal axis ranging from 0 to 10. This will represent the possible values of our variable.

- Identify the Mean

The problem specifies that the mean is 5, so this value should be in the middle of our graph. Place a mark at 5 on the horizontal axis to indicate this.

- Identify the Standard Deviation

The standard deviation is given to be 2. On a normal distribution, approximately 68% of values will fall within one standard deviation of the mean. If the mean is 5 and standard deviation is 2, marks should be placed at 3 (5-2) and 7(5+2) to represent one standard deviation each side of the mean.

Draw the Curve

Finally, draw a smooth, symmetrical curve that reaches its peak at the mean (5), and tails off as you move farther away from the mean. The inflection points of the curve should be at the one standard deviation marks (3 and 7).