<PRE><B>Question 1150804</B>
&lt;pre&gt;Get a TI-83 or TI-84 calculator

Press 2ND VARS 1

The lower value is 5.7
The upper value is 7.5
The µ is 6
The σ is 3

Once you have this:

normalcdf(5.7,7.5,6,3)

press ENTER

read 0.231290364 and round to 0.2313

If you must do it the old fashioned way (with a table), you want to know
what decimal fraction the shaded part (between the two z-values for x=5.7
and x=7.5, which we must calculate) is:

{{{drawing(400,200,-5,5,-.5,1.5, graph(400,200,-5,5,-.5,1.5, exp(-x^2/2)),
line(-0.1,0.99501248,-0.1,0),line(-0.09,0.99595819,-0.09,0),line(-0.08,0.99680511,-0.08,0),line(-0.08,0.99680511,-0.08,0),
line(-0.07,0.997553,-0.07,0),line(-0.06,0.99820162,-0.06,0),line(-0.05,0.99875078,-0.05,0),line(-0.05,0.99875078,-0.05,0),
line(-0.04,0.99920032,-0.04,0),line(-0.03,0.9995501,-0.03,0),line(-0.02,0.99980002,-0.02,0),line(-0.02,0.99980002,-0.02,0),
line(-0.01,0.99995,-0.01,0),line(-0.10408341e-16,1.0,-0.10408341e-16,0),line(0.01,0.99995,0.01,0),line(0.01,0.99995,0.01,0),
line(0.02,0.99980002,0.02,0),line(0.03,0.9995501,0.03,0),line(0.04,0.99920032,0.04,0),line(0.04,0.99920032,0.04,0),
line(0.05,0.99875078,0.05,0),line(0.06,0.99820162,0.06,0),line(0.07,0.997553,0.07,0),line(0.07,0.997553,0.07,0),
line(0.08,0.99680511,0.08,0),line(0.09,0.99595819,0.09,0),line(0.1,0.99501248,0.1,0),line(0.1,0.99501248,0.1,0),
line(0.11,0.99396826,0.11,0),line(0.12,0.99282586,0.12,0),line(0.13,0.9915856,0.13,0),line(0.13,0.9915856,0.13,0),
line(0.14,0.99024786,0.14,0),line(0.15,0.98881304,0.15,0),line(0.16,0.98728157,0.16,0),line(0.16,0.98728157,0.16,0),
line(0.17,0.9856539,0.17,0),line(0.18,0.98393051,0.18,0),line(0.19,0.98211193,0.19,0),line(0.19,0.98211193,0.19,0),
line(0.2,0.98019867,0.2,0),line(0.21,0.97819132,0.21,0),line(0.22,0.97609047,0.22,0),line(0.22,0.97609047,0.22,0),
line(0.23,0.97389674,0.23,0),line(0.24,0.97161077,0.24,0),line(0.25,0.96923323,0.25,0),line(0.25,0.96923323,0.25,0),
line(0.26,0.96676484,0.26,0),line(0.27,0.9642063,0.27,0),line(0.28,0.96155838,0.28,0),line(0.28,0.96155838,0.28,0),
line(0.29,0.95882184,0.29,0),line(0.3,0.95599748,0.3,0),line(0.31,0.95308613,0.31,0),line(0.31,0.95308613,0.31,0),
line(0.32,0.95008863,0.32,0),line(0.33,0.94700586,0.33,0),line(0.34,0.9438387,0.34,0),line(0.34,0.9438387,0.34,0),
line(0.35,0.94058806,0.35,0),line(0.36,0.9372549,0.36,0),line(0.37,0.93384015,0.37,0),line(0.37,0.93384015,0.37,0),
line(0.38,0.93034481,0.38,0),line(0.39,0.92676987,0.39,0),line(0.4,0.92311635,0.4,0),line(0.4,0.92311635,0.4,0),
line(0.41,0.91938529,0.41,0),line(0.42,0.91557774,0.42,0),line(0.43,0.91169479,0.43,0),line(0.43,0.91169479,0.43,0),
line(0.44,0.90773754,0.44,0),line(0.45,0.90370708,0.45,0),line(0.46,0.89960455,0.46,0),line(0.46,0.89960455,0.46,0),
line(0.47,0.8954311,0.47,0),line(0.48,0.89118789,0.48,0),line(0.49,0.88687609,0.49,0),line(0.49,0.88687609,0.49,0) )}}}

We calculate the z-score for the right-most value 7.5:

{{{z=(x-mu)/sigma=(7.5-6)/3=0.5}}}

We calculate the z-score for the left-most value 5.7:

{{{z=(x-mu)/sigma=(5.7-6)/3=-0.1}}}

If your table is the newer kind with negative z-values, 
look up z=0.50 in the z-column and the 0 column should read 0.6915.
look up z=-0.10 in the z-column and the 0 column should read 0.4602.
Subtract 0.6915-0.4602 = 0.2313.

If your table is the older kind with no negative z-values, 
look up z=0.50 in the z-column and the 0 column should read 0.1915.
look up z=0.10 in the z-column and the 0 column should read 0.0398.
Add 0.1915+0.0398 = 0.2313.

Sometimes the calculator method will differ in the last decimal place
because the calculator is more modern and accurate than the old-fashioned
table.

Edwin&lt;/pre&gt;
 </PRE>