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:



We calculate the z-score for the right-most value 7.5:



We calculate the z-score for the left-most value 5.7:



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