Question

How does changing the mean affect a normal distribution? How does changing the standard deviation affect a normal distribution?

Answer 1

The mean of a distribution informs us of "center"; the standard deviation of a distribution informs us of "spread". The mean of a normal distributionrepresents the value at which the probability is at its peak, and the shape of the graph is a bell-curve; increasing or decreasing the mean withoutchanging standard deviation then simply moves the bell-curve to the right or to the left. An increased standard deviation, in contrast, does not change themean, but spreads out the graph so that it includes more values. Decreasing the standard deviation would bring the graph closer to the mean values.

Answer 2

http://www-stat.stanford.edu/~naras/jsm/NormalDensity/NormalDensity.html