What sort of applications does the normal distribution have in electrical engineering?
I'll give one example:

Here's a plot from the datasheet of Analog Devices AD8659 precision operational amplifier (or op-amp). This shows the distribution of a parameter called input offset voltage over a sample of a few hundred individual amplifiers. 



In a working circuit, the offset voltage typically contributes an error to a measurement when the op-amp is being used for signal conditioning, or in a feedback variable when the op-amp is being used in a control loop. 

When you're designing a circuit with this op-amp, you might model this distribution fairly accurately with a normal distribution, and do a Monte Carlo analysis to find out how the performance of your whole circuit is likely to be distributed in response to this variation in the op-amp performance as well as other variables in other components in the circuit.