With a normal distribution, it's possible to figure out the fraction of the total that fall between limits. In fact, you can find tables that show you the percentage of the area that lies between fractions of the standard deviation. Since you know the mean and the standard deviation, you can use those tables (or the formula that is used to draw the curve) to answer your question:
Distribution Tables
http://www.math.umn.edu/~armstron/4707/Z-Values.pdf
Note that the mean was 4.2 minutes and the standard deviation was 0.6 minutes. 5 minutes is (5-4.2)/0.6 = 1.333 standard deviations from the mean. So, to answer a), all you have to do is look at the tables and find the fraction of area between the mean and 1.333 standard deviations from the mean.
Once you do that, the other answers are simply extensions of this method.