'normally distributed random numbers' vs 'uniformly distributed random number'? what is the difference between 'normally distributed random numbers' and 'uniformly distributed random number'? A answer in a layman language is appreciated :) 
 A: 
The green line shows a uniform distribution over the range $[-5, 5]$.  Informally, each number in the range is equally ("uniformly") likely to be picked.  
The red line shows a normal distribution with mean of 0 and standard deviation of 1.  Numbers close to the mean are much more likely to be picked than those far away from the mean, in a particular and very special way.
The special thing about the normal distribution is this:  If you take a large number of samples from a population with any distribution (subject to some not very strict conditions) and average them, the resulting distribution will approximate a normal distribution.  For example, if you roll many dice and average the result, the resulting number will be distributed normally. The more dice you use, the closer the result will be to a normal distribution.
This property is why the normal distribution appears in nature.  People's heights, for example, are normally distributed, because there are a large number of random factors that affect a person's height, but when they're all added together, the result is normal.
