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The CDF of any normal variable can be expressed through the standard normal CDF . See the Wiki page and also this similar thread.
Since in your example the maximum allowed deviation 0.5cm is twice the standard deviation , you need to find . If you express through , you'll get rid of and . See also the Wiki section on confidence intervals.
Even though this problem is from discrete mathematics class, the problem itself is purely probability theory. In the future, you'll have more chances to get a good reply if you post it to either basic or advanced statistics and probability section.