This is a binomial problem with




You are asked:

What is the probability that between 50% and 60% of them 
will graduate in 5 years or less?

Since 50% of 500 is 250 and 69% of 500 is 300, this is the
same as being asked

What is the probability that between 250 and 300 of the 500 
will graduate in 5 years or less?

You can do this on a TI-83 or TI-84 by

binomcdf(500,.53,300) - binomcdf(500,.53,250)

getting .902291559.

Or you can do it by approximating the binomial with the normal.






normalcdf(249.5,300.5,265,11.16019713)

getting .916828909

Or if your teach won't let you use a calculator and insists on
less accurate tables, then find the z-scores of

249.5 and 300.5,













and, depending on what kind of table you have, you will
either 

1. If your table has only positive z-scores,

look up 1.38, finding .4162, look up 3.18, finding .4993,
add these and get .9155

or 

2. If your table has both positive and negative z-scores,

look up -1.38, finding .0838, look up 3.18, finding .9993,
subtract these and get .9155.

Edwin