SOLUTION: One environmental group did a study of recycling habits. It found that 74% of aluminum cans were recycled. If 392 cans are recycled what is the probability that 300 or more are c

In the first part, you incorrectly interpreted "300 or more are cycled" as 
"more than 300".  But 300 IS included. To include 300, you must 
use (>299.5) not (>300.5), because (>300.5) does NOT include the case 
when exactly 300 are cycled, whereas (>299.5) does.

The correct answer is .1390

In the second part there must be a subtraction,  I will assume that
by 260-300 you mean to INCLUDE both 260 and 300. 


(< 300.5) - (< 259.5) = .8849 - .0002 = .8847

You must be careful to observe whether you are to INCLUDE or NOT to
INCLUDE the endpoint.  

If the interval is A to B, it's

(< A-.5) - (< B+.5)  if you are including both endpoints.

and

(< A+.5) - ( B-.5)  if you are NOT including either endpoint.

Edwin