Question 1154524
<pre>
P(-2.14 < z < 0.95)

Notice that the shading below starts where z=-2.14 and goes to where z=0.95.
We want to know what decimal or percentage of the curve is shaded below

{{{drawing(400,200,-5,5,-.5,1.5, graph(400,200,-5,5,-.5,1.5, exp(-x^2/2)),
locate(4.8,.2,z),
line(-2.14,0,-2.14,0.10128672),line(-2.04,0,-2.04,0.12483031),line(-1.94,0,-1.94,0.15231569),line(-1.94,0,-1.94,0.15231569),
line(-1.84,0,-1.84,0.18400359),line(-1.74,0,-1.74,0.22007211),line(-1.64,0,-1.64,0.26059182),line(-1.64,0,-1.64,0.26059182),
line(-1.54,0,-1.54,0.30550168),line(-1.44,0,-1.44,0.35458755),line(-1.34,0,-1.34,0.4074651),line(-1.34,0,-1.34,0.4074651),
line(-1.24,0,-1.24,0.46356902),line(-1.14,0,-1.14,0.5221502),line(-1.04,0,-1.04,0.58228224),line(-1.04,0,-1.04,0.58228224),
line(-0.94,0,-0.94,0.6428782),line(-0.84,0,-0.84,0.70271772),line(-0.74,0,-0.74,0.76048416),line(-0.74,0,-0.74,0.76048416),
line(-0.64,0,-0.64,0.81481026),line(-0.54,0,-0.54,0.86433055),line(-0.44,0,-0.44,0.90773754),line(-0.44,0,-0.44,0.90773754),
line(-0.34,0,-0.34,0.9438387),line(-0.24,0,-0.24,0.97161077),line(-0.14,0,-0.14,0.99024786),line(-0.14,0,-0.14,0.99024786),
line(-0.04,0,-0.04,0.99920032),line(0.06,0,0.06,0.99820162),line(0.16,0,0.16,0.98728157),line(0.16,0,0.16,0.98728157),
line(0.26,0,0.26,0.96676484),line(0.36,0,0.36,0.9372549),line(0.46,0,0.46,0.89960455),line(0.46,0,0.46,0.89960455),
line(0.56,0,0.56,0.85487502),line(0.66,0,0.66,0.80428628),line(0.76,0,0.76,0.74916202),line(0.76,0,0.76,0.74916202),
line(0.86,0,0.86,0.69087249)



)}}}

So by TI-83 or 84 calculator, we press " 2nd " then " vars " then " 2:normalcdf( "

[for newer calculators, lower:-2.14, upper:0.95, &mu;=0; &sigma;=1; paste, enter]

For all calculators:

normalcdf(-2.14,0.95,0,1)

press ENTER

0.8127665627

With tables:  [There are two kinds of tables in use today]

If your table has negative numbers in the z-column, then
find 0.9 in the z-column and go across to the 0.05 column and read 0.8289
find -2.1 in the z-column and go across to the 0.04 column and read 0.0162
Subtract and get 0.8289-0.0162 and get 0.8127

If your table has only positive numbers in the z-column, then
find 0.9 in the z-column and go across to the 0.05 column and read 0.3289
find 2.1 in the z-column and go across to the 0.04 column and read 0.4838
Add them and get 0.3289+0.4838 and get 0.8127


Notice that the calculator answers round to 0.8128, whereas with
tables you get 0.8127.  That's because the calculator is more accurate
than tables.

Edwin</pre>