Question 1039491
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The mean is 530
1 standard deviation below the mean is 530-88 = 442
2 standard deviations below the mean is 442-88 = 354
3 standard deviations below the mean is 354-88 = 266

So 266 is 3 standard deviations below the mean.

The mean is 530
1 standard deviation above the mean is 530+88 = 618
2 standard deviations above the mean is 618+88 = 706
3 standard deviations above the mean is 706+88 = 794

So 794 is 3 standard deviations above the mean.

On this graph:

{{{drawing(400,200,-5,5,-.5,1.5, graph(400,200,-5,5,-.5,1.5, exp(-x^2/2)),locate(4.8,-.01,z),locate(4.8,.2,z)

)}}}

0 on the horizontal z-axis represents the mean, 530
-1 on it represents 1 standard deviation below the mean, 442.
-2 on it represents 2 standard deviations below the mean or 354.
-3 on it represents 3 standard deviations below the mean or 266.
1 on it represents 1 standard deviation above the mean, 618.
2 on it represents 2 standard deviations above the mean or 706.
3 on it represents 3 standard deviations above the mean or 794.

The EMPIRICAL RULE (or the 68-95-99.7 Rule) says that about 68% of the data is between
1 standard deviation below the mean and 1 standard deviation above
the mean.  Below the shaded part is about 68% of the area between
the normal curve and the z-axis.

{{{drawing(300,150,-5,5,-.5,1.5, graph(300,150,-5,5,-.5,1.5, exp(-x^2/2)),
locate(4.8,-.01,z),locate(4.8,.2,z),line(-1,0,-1,0.60653066),line(-0.9,0,-0.9,0.66697681),line(-0.8,0,-0.8,0.72614904),line(-0.7,0,-0.7,0.78270454),line(-0.6,0,-0.6,0.83527021),line(-0.5,0,-0.5,0.8824969),line(-0.4,0,-0.4,0.92311635),line(-0.3,0,-0.3,0.95599748),line(-0.2,0,-0.2,0.98019867),line(-0.1,0,-0.1,0.99501248),line(0,0,0,1.0),line(0.1,0,0.1,0.99501248),line(0.2,0,0.2,0.98019867),line(0.3,0,0.3,0.95599748),line(0.4,0,0.4,0.92311635),line(0.5,0,0.5,0.8824969),line(0.6,0,0.6,0.83527021),line(0.7,0,0.7,0.78270454),line(0.8,0,0.8,0.72614904),line(0.9,0,0.9,0.66697681),line(1.0,0,1.0,0.60653066),locate(20,20,1))}}}

The EMPIRICAL RULE (or the 68-95-99.7 Rule) also says that about 95%
of the data is between 2 standard deviations below the mean and 2 
standard deviations above the mean.  Below the shaded part is about 
95% of the area between the normal curve and the z-axis.

{{{drawing(300,150,-5,5,-.5,1.5, graph(300,150,-5,5,-.5,1.5, exp(-x^2/2)),
locate(4.8,-.01,z),locate(4.8,.2,z),line(-2,0,-2,0.13533528),line(-1.9,0,-1.9,0.16447446),line(-1.8,0,-1.8,0.1978987),line(-1.7,0,-1.7,0.23574608),line(-1.6,0,-1.6,0.2780373),line(-1.5,0,-1.5,0.32465247),line(-1.4,0,-1.4,0.3753111),line(-1.3,0,-1.3,0.42955736),line(-1.2,0,-1.2,0.48675226),line(-1.1,0,-1.1,0.54607443),line(-1.0,0,-1.0,0.60653066),line(-0.9,0,-0.9,0.66697681),line(-0.8,0,-0.8,0.72614904),line(-0.7,0,-0.7,0.78270454),line(-0.6,0,-0.6,0.83527021),line(-0.5,0,-0.5,0.8824969),line(-0.4,0,-0.4,0.92311635),line(-0.3,0,-0.3,0.95599748),line(-0.2,0,-0.2,0.98019867),line(-0.1,0,-0.1,0.99501248),line(0,0,0,1.0),line(0.1,0,0.1,0.99501248),line(0.2,0,0.2,0.98019867),line(0.3,0,0.3,0.95599748),line(0.4,0,0.4,0.92311635),line(0.5,0,0.5,0.8824969),line(0.6,0,0.6,0.83527021),line(0.7,0,0.7,0.78270454),line(0.8,0,0.8,0.72614904),line(0.9,0,0.9,0.66697681),line(1.0,0,1.0,0.60653066),line(1.1,0,1.1,0.54607443),line(1.2,0,1.2,0.48675226),line(1.3,0,1.3,0.42955736),line(1.4,0,1.4,0.3753111),line(1.5,0,1.5,0.32465247),line(1.6,0,1.6,0.2780373),line(1.7,0,1.7,0.23574608),line(1.8,0,1.8,0.1978987),line(1.9,0,1.9,0.16447446),locate(20,20,1))}}}

The EMPIRICAL RULE also says that about 99.7% of the data is between
3 standard deviations below the mean and 3 standard deviations above
the mean.  Below the shaded part is about 99.7% of the area between
the normal curve and the z-axis.  (That's roughly ALL of it!)

{{{drawing(300,150,-5,5,-.5,1.5, graph(300,150,-5,5,-.5,1.5, exp(-x^2/2)),
locate(4.8,-.01,z),locate(4.8,.2,z),line(-3,0,-3,0.011108997),line(-2.9,0,-2.9,0.014920786),line(-2.8,0,-2.8,0.019841095),line(-2.7,0,-2.7,0.02612141),line(-2.6,0,-2.6,0.034047455),line(-2.5,0,-2.5,0.043936934),line(-2.4,0,-2.4,0.056134763),line(-2.3,0,-2.3,0.071005354),line(-2.2,0,-2.2,0.088921617),line(-2.1,0,-2.1,0.11025053),line(-2.0,0,-2.0,0.13533528),line(-1.9,0,-1.9,0.16447446),line(-1.8,0,-1.8,0.1978987),line(-1.7,0,-1.7,0.23574608),line(-1.6,0,-1.6,0.2780373),line(-1.5,0,-1.5,0.32465247),line(-1.4,0,-1.4,0.3753111),line(-1.3,0,-1.3,0.42955736),line(-1.2,0,-1.2,0.48675226),line(-1.1,0,-1.1,0.54607443),line(-1.0,0,-1.0,0.60653066),line(-0.9,0,-0.9,0.66697681),line(-0.8,0,-0.8,0.72614904),line(-0.7,0,-0.7,0.78270454),line(-0.6,0,-0.6,0.83527021),line(-0.5,0,-0.5,0.8824969),line(-0.4,0,-0.4,0.92311635),line(-0.3,0,-0.3,0.95599748),line(-0.2,0,-0.2,0.98019867),line(-0.1,0,-0.1,0.99501248),line(0,0,0,1.0),line(0.1,0,0.1,0.99501248),line(0.2,0,0.2,0.98019867),line(0.3,0,0.3,0.95599748),line(0.4,0,0.4,0.92311635),line(0.5,0,0.5,0.8824969),line(0.6,0,0.6,0.83527021),line(0.7,0,0.7,0.78270454),line(0.8,0,0.8,0.72614904),line(0.9,0,0.9,0.66697681),line(1.0,0,1.0,0.60653066),line(1.1,0,1.1,0.54607443),line(1.2,0,1.2,0.48675226),line(1.3,0,1.3,0.42955736),line(1.4,0,1.4,0.3753111),line(1.5,0,1.5,0.32465247),line(1.6,0,1.6,0.2780373),line(1.7,0,1.7,0.23574608),line(1.8,0,1.8,0.1978987),line(1.9,0,1.9,0.16447446),line(2.0,0,2.0,0.13533528),line(2.1,0,2.1,0.11025053),line(2.2,0,2.2,0.088921617),line(2.3,0,2.3,0.071005354),line(2.4,0,2.4,0.056134763),line(2.5,0,2.5,0.043936934),line(2.6,0,2.6,0.034047455),line(2.7,0,2.7,0.02612141),line(2.8,0,2.8,0.019841095),line(2.9,0,2.9,0.014920786),locate(20,20,1))}}}

Edwin</pre>