The normal distribution has two parameters, the mean mu and the standard deviation sigma.
parameters are known, the distribution is completely specified. Although the standard deviation is a positive number,
the mean can assume any value. The distribution is symmetrical with mean,
mode, and median all equal at mu.
The normal distribution is one which appears in a
variety of statistical applications. One reason
for this is the central limit theorem. This theorem tells us that
sums of random variables are approximately normally distributed if the
number of observations is large. For example, if we toss a coin, the total
number of heads approaches normality if we toss the coin a lot of times.
Even when a distribution may not be exactly normal, it may still
be convenient to assume that a normal distribution is a good
approximation. In this case, many statistical procedures, such as the
t-test,or ANOVAcan still be used.