Evaluating probabilities for a Normal Distribution used to be done with tables. However, some exam boards are now allowing the use of calculators to replace the use of tables making it a lot easier and quicker.
The Normal Cumulative Distribution function on a Casio Classwiz calculator evaluates the P(a<X<b) for a random variable X which follows a Normal Distribution.
Many calculators have similar functions so do check out your manual.
Using a Calculator