C. Area under a Normal Curve

Open the Normal Distribution applet (6 March 2013, Created with GeoGebra) and complete the following to further explore the normal curve.

Use the sliders to see the area under the normal curve between two points. The left and right arrow keys can be used to finely adjust the sliders.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com


  1. Try changing the mean and the standard deviation. Describe how changing each affects the normal curve.

  2. Select the "show area between x-values" box on the applet. Use the four sliders to complete the following table.

    ยต
    		 ฯƒ
    x1
    number of standard
    deviations x1 is from
    the mean
    x2
    number of standard
    deviations x2 is from
    the mean
    area under the
    curve between
    x1 and x2
    4
    1
    3
    		 1 SD below the mean
    5
    		 1 SD above the mean
    0.6383
    4
    1
    2
    		 2 SD below the mean
    6
    		 2 SD above the mean
    4
    1
    1
    7
    5
    0.5
    4.5
    		 1 SD below the mean
    5.5
    		 1 SD above the mean
    5
    0.5
    		2 SD below the mean
    		2 SD above the mean
    5
    0.5
    		3 SD below the mean
    		3 SD above the mean
    8
    3
    5
    		 1 SD below the mean
    11
    		 1 SD above the mean
    8
    3
    2
    14
    8
    3
    -1
    17


    1. Predict the area under any normal curve that is within 1 standard deviation of the mean.
    2. Predict the area under any normal curve that is within 2 standard deviations of the mean.
    3. Predict the area under any normal curve that is within 3 standard deviations of the mean.