The normal distribution is typically used in situations where there is little or no scope uncertainty, and there is an expected cost or established rate for the work to be done. This is represented by the base or mid-range estimate at the peak of the distribution.
A normal distribution is symmetrical about the peak. Modelling a cost with a normal distribution indicates a belief that the actual cost is just as likely to be a given amount under the mid-range estimate as over the mid-range estimate.
A normal distribution theoretically extends indefinitely on either side of the peak, so wherever you place the contingency limit or high-range value, there will always be some probability, however small, of overrunning this limit.