STA301 GDB no 1 Fall 2011 Idea Solution

“Normal distribution is symmetric with a single peak. Does this means that all symmetric distribution are normal. Explain.”
Solution:

The normal distributions are a very important class of statistical distributions. All normal distributions are symmetric and have bell-shaped density curves with a single peak. Both the normal and Symmetrical distributions are U-shaped and equal from both sides.

The Normal distribution:
It is considered the most prominent probability distribution in statistics. There are several reasons for this:

First, the normal distribution is very tractable analytically, that is, a large number of results involving this distribution can be derived in explicit form.
Second, the normal distribution arises as the outcome of the central limit therorem, which states that under mild conditions the sum of a large number of random variables is distributed approximately normally.
Finally, the “bell” shape of the normal distribution makes it a convenient choice for modelling a large variety of random varibales encountered in practice.

Definition of “Symmetrical distribution”

A situation in which the values of varibale occur at regular frequencies, and the mean, median and mode occur at the same point. Unlike asymmetrical A distribution, symmetrical distribution does not skew. A symmetrical distribution is commonly shaped like a bell curve when depicted on a graph. If a line is drawn the middle of the graph, the two sides will mirror each others. Symmetric distribution is also called normal distribution.