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 0.5

Short answer

First, a horizontal scale from 0 to 10 was set. The curve was drawn so that the peak corresponds to the mean value (5), and the width of the bell-like figure is influenced by the standard deviation (approximately 0.5). The curve was then finished symmetrically, tapering off to approach the horizontal axis without touching it.

Step-by-step solution

- Set Up the Horizontal Axis

Draw a horizontal line from 0 to 10. This line will represent the axis in which we will draw the curve. Then, divide this line into 10 equal segments since the maximum value is the 10. Consequently, each segment represents one unit.

- Draw the Center of the Curve

From the mean value, which is 5, draw a vertical line. This will be the location of the center of the curve or where the curve reaches its peak (as it's the maximum point in a Normal Distribution).

- Draw the Curves flanks

Starting from the peak of the curve at the mean, draw the descending flanks of the curve on both sides. The width of the curve will be determined by the standard deviation, which is 0.5 in this case. The rule of thumb is that approximately 68% of the data lies within 1 standard deviation from the mean in a Normal Distribution curve. Therefore, at approximately 4.5 and 5.5 on the scale, the curve should transition from its descending slope to nearly horizontal. The exact positioning of these points requires an understanding of probability and mathematical calculation.

- Completing the Curve

After drawing the descending flanks, complete the drawing by creating a curve that tapers off and approaches, but never quite reaches, the horizontal axis. To make the curve symmetric, make sure both sides of it (right and left) look the same.