# Normal

#### Description

This sketch allows you to change the parameters of a normal curve and compute the area under any portion of it.

The formula for the normal curve is shown above. There are three parameters to change, each corresponding to a point in the sketch.

- The parameter
*A*controls the maximum height of the curve, which is . You can drag the point at the top of the curve to change its height. - The mean (μ in the formula) is controlled by the point labeled mean in the sketch.
- The standard deviation is σ.

Press *Show Integral* to get two control points, *x _{i}* and

*x*. The area under the curve between these two values will be shown in pink and computed numerically.

_{f}#### Questions

- Demonstrate the assertion that about two-thirds of the area under a normal curve lies within plus or minus one standard deviation of the mean.
- Use the sketch to find the proportion of the area under the curve that lies to the right of the mean plus one standard deviation.
- Lengths of tadpoles in a certain pond are found to be approximately normally distributed with a mean of 1.25 inches and a standard deviation of .25 inches. Use the sketch to find the chances of finding a tadpole with a length greater than 1.75 inches.