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Finding Area Under a Normal Curve

Example: A pediatrician obtains the heights of her 200 three-year-old female patients.  The heights are normally distributed, with mean 38.72 and standard deviation 3.17.  What percent of the three-year-old females have a height less then 35 inches?

In this exercise, use a normal distribution with  and

Method 1:  To find the percent of three-year-old females with heights less than 35 inches we calculate

  Press 2^nd [DISTR], select 2:normalcdf( and type in -1E99 , 35 , 38.72 , 3.17 ) and press ENTER.

Method 2:  To find the and include a graph, you must first set up the WINDOW so that the graph will be displayed properly.  You will need to set Xmin 3qual to   and Xmax equal to .  Press WINDOW and set Xmin equal to  by typing in 38.72 -3 * 3.17.  Set Xscl equal to , which is 3.17.

Setting the Y-range is a little more difficult to do.  A good “rule-of-thumb” is to set Ymax equal to

.  For this example, set Ymax = .5/3.17.

Use the blue up arrow to highlight Ymin.  A good value for Ymin is (-) Ymax / 4 so type in

(-) .158 / 4.

Press 2^nd [DRAW] and select 1:ClrDraw and press ENTER ENTER.  Press 2^nd [STATPLOT] and TURN OFF all PLOTS.  Press 2^nd [DISTR], highlight DRAW and select 1:ShadeNorm( and type

in -1E99 , 35 , 38.72 , 3.17 ) and press ENTER.

Conclusion:  12.0% of all three-year-old females are less than 35 inches tall.

Note:  When using the TI-83 (or any other technology tool), the answers you obtain may vary slightly from the answers that you would obtain using the standard normal table.  Consequently, your answers may not be exactly the same as the answers found in your textbook.  The differences are simply due to rounding.