Normal Distribution

Normal Distribution
l The most important continuous probability
distribution in the entire field of statistics is normal
distribution and it is frequently called Gaussian
distribution.
l The normal distribution depends on the values of,

Normal Distribution
l • If a random variable X has the Normal distribution with mean ? and
variance, this is denoted by:
l X ~N (?, ).
l • In order to obtain probabilities for the Normal distribution (i.e. areas
under the curve), it is necessary to express any value of X in terms of
the number of standard deviation units it is away from ?.
l i.e; X=?+z
l or Z=(X- ? )/
s 2
s 2
s
s
Standard Normal distribution
•The Standard Normal distribution has a mean of 0 and a SD of 1,
Z~N(0,1)
• Probabilities for Normal distributions other than the standard Normal
distribution N (0, 1) are obtained by using the formula,
Z=X- ? /s
to convert from normal distribution X ~ N (?, s ) to standard normal
distribution Z ~ N(0,1) and then using the table of probabilities for
N(0,1).
Total area under the curve=1
The values inside the given table represent the areas under the
standard normal curve for values between 0 and the relative z-score.