Dear Zachary Chasse,
A visual may help you out here...because in a normal distribution of data, the points will cluster in a classic bell-shaped curve around one average value - known as the mean, and symbolized as lower-case mu (Greek letter).
And one standard deviation from that mean, designated lower-case sigma, will contain 68.2% of all the values. So if the standard deviation is large, the bell will be short and spread out; if small, then the curve will be tall and narrow.
As you see, your standard deviation of fifteen will thus contain IQ scores ranging between 105 and 135.