calculate z-score for lower bound 



That rounds to -1.79

calculate z-score for upper bound 



That rounds to -0.71

Now whichever way you go from here depends on what kind
of table you have, or whether you use a calculator.
Different books have different kinds of normal tables.  

If your normal table has negative values of z listed:
    1.  Find -0.7 in the z column.
    2.  Go across until you are under the .01 column
    3.  Read 0.2389 as the area left of -0.7
    4.  Find -1.7 in the z column.
    5.  Go across until you are under the .09 column
    6.  Read 0.0367 as the area left of -1.79  
    7.  Subtract 0.2389-0.0367
    8.  Get 0.2022

If your normal table does not have negative values of z
listed:
    1.  Find 0.7 in the z column.
    2.  Go across until you are under the .01 column
    3.  Read 0.2611 as the area between 0.5 and 0.71
    4.  Find 1.7 in the z column.
    5.  Go across until you are under the .09 column
    6.  Read 0.4633 as the area between 0.5 and 1.79  
    7.  Subtract 0.4633-0.2611
    8.  Get 0.2022 

Either way the probability is 0.2022.  However, this is only 
accurate to two decimal places, since 0.71 was only accurate
to two decimal places, so we should round off to 0.20.

If you have a TI-84 calculator:

Clear the calculator and get on the main screen
Press 2nd
Press VARS
Press 2
You should see normalcdf(
after that parentheses type this 55.0,70.0,80.0,14.0)
You should see normalcdf(55.0,70.0,80.0,14.0)
Press ENTER
Read 0.2004524729

The calculator is much more accurate than the table.

Edwin