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 3 and standard deviation 1.

Short answer

To plot the normal distribution curve, one starts by marking the mean (3 in this case) on the x-axis. One standard deviation (1 in this instance) is then marked on either side of the mean, resulting in points at 2 and 4. The bell curve is then drawn symmetrically about the mean, stretching approximately 3 standard deviations on either side. Normally, about 99.7% of data falls within three standard deviations of the mean in a normal distribution.

Step-by-step solution

Label the Axis

Draw an x-axis from scale 0 to 10. Label this horizontal line as 'x'.

Mark the Mean

Locate and mark the mean value, which is 3, on the x-axis. This is the central point around which the curve will be symmetric.

Mark the Standard Deviations

Starting from the mean value, mark the points that are 1 standard deviation away. Do this each side of the mean. Mark these points as 2 and 4, in this case, each representing one standard deviation unit away from the mean.

Sketch the Curve

Draw a symmetric, bell-shaped curve centered around the mean value, gradually tapering off as it moves farther away from the mean on both the sides. Make sure that the curve touches the x-axis at approximately three standard deviations from the mean. This will ensure the curve is within the scales of 0 to 10.