Question 177721
I will help you with part a) and you can work on the rest.  The first step in trying to compute a probability like this is standardizing the values.  Remember, this is done by subtracting the mean and dividing by the standard deviation.  For example, 60 would be (60-60)/6=0 (the mean is always 0 standardized).  Similarly, 69 would be (69-60)/6=1.5.  So what the question is really asking is "what is the area under the normal curve between 0 and 1.5?"  Well, if we use a table to look up 1.5, such as http://www.sjsu.edu/faculty/gerstman/EpiInfo/z-table.htm 
we get that the area to the left of 1.5 is 0.9332, or 93.32%.  But what we're looking for is just between 0 and 1.5.  Remember that the normal curve is symmetrical about 0, so the area to the left of 0 is exactly half, or 0.5 (or 50%).  So if we subtract 50% from 93.32%, we'll get the area in between 0 and 1.5.  So the probability of a value between 60 and 69 is 43.32%.  Hope that helps.