Page 46 - Basic Statistics

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A continuous random variable X which has a bell-shaped distribution as in

Figure 3.1 is called a normal random variable. The mathematical equation for
the probability distribution of normal random variable is determined by two

parameters  and  , namely the mean and standard deviation. Therefore we

symbolize the values of density function for X is n(x;  ,  ).

2
If X is a normal random variable with a mean value  and variance  ,
then the equation of the normal curve is

1 1 −  2
n(x;  ,  ) = e − 2 (  ) , untuk -  < x <  , ( Z1 )
2  

whereas in this case  = 3.14159… and e = 2.71828.

3.2 AREA UNDER THE NORMAL CURVE

Curves of any continuous probability distribution or density functions

are such that the area under the curve was constrained by x = x1 and x = x2 is
equal to the probability that a random variable X taking values between by x =

x1 and x = x2. Thus, the normal curve in Figure 3.2. P(x1 < X < x2 ) is expressed

by the area shaded.

Figure 3.2. P( x1 < X < x2 ) is expressed by the area shaded

~~* CHAPTER 3 NORMAL PROBABILITY DISTRIBUTION *~~