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Finding Area Under the Standard Normal Curve Left of a Z-score

Example:  Find the area under the standard normal curve that lies to the left of

Method 1:  Normalcdf(lowerbound, upperbound, ) computes the area between a lowerbound and an upperbound.  In this example, you are computing the area from negative infinity to 1.68.  Negative infinity is specified by   (-) 1 2^nd [EE] 9 9 (Note:  EE is found above the comma , ).  Try entering -1 EE 99 into your calculator.

Now, to calculate the area to the left of 1.68, press 2^nd [DISTR] and select 2:normalcdf(and type in -1E99 , 1.68 , 0 , 1 ) and press ENTER.  (Note:  For the standard normal curve,   and

Method 2:  This method calculates the area and also displays a graph of the probability distribution.  You must first set up the WINDOW so that the graph will be displayed properly.  Press WINDOW and set Xmin equal to -3 and set Xmax equal to 3.  Set Xscl equal to 1.

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. 

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

 (-) .5 / 4.

Press 2^nd [QUIT].  Clear all the previous drawings by pressing 2^nd [DRAW] and selecting 1:ClrDraw and pressing ENTER ENTER.  Press 2^nd [STATPLOT] and TURN OFF all PLOTS.  Now you can draw the probability distribution.  Press 2^nd [DISTR].  Highlight DRAW and select 1:ShadeNorm(and type in -1E99 , 1.68 , 0 , 1 ) and press ENTER.  The output displays a normal curve with the appropriate area shaded in and its value computed.