Standard Deviation: Can someone show me how to work this statistical problem out?

You pretty much need to use z-tables for these kind of problems. Or you could look up the equation for the normal distribution and integrate it with a computer. If you want to do it manually you will get an error function when you integrate, and those are pretty tough to deal with. Your best bet to do something manually with this type of problem would just look up the values in a z-table.