Compare a graph of the normal density function with mean of 0 and standard deviation of 1 with a graph of anormal density function with mean equal to 0 and standard deviation of 0.5. The graphs would
A) Have no horizontal displacement but one would be steeper that the other.
B) Have no horizontal displacement but one would be flatter than the other.
C) Have the same height but one would be shifted 4 units to the right.
D) Have the same height but one would be shifter 4 units to the left.

Question

Quizplus · Accepted Answer

The mean determines the horizontal location of the peak of the normal distribution, so both graphs, having a mean of 0, would not be horizontally displaced relative to each other. The standard deviation affects the spread of the distribution: a smaller standard deviation (0.5) results in a steeper graph compared to a standard deviation of 1.

Compare a Graph of the Normal Density Function with Mean