Some of these curves are Bell-Shaped. W e call them Normal Curves. Normal distribution is bell shaped ( unimodal ) and Symmetric. The mean, median and mode are all located at the center of the distribution. The curve is continuous and never touches the X - axis. The equation of the Bell-shaped curve is
where x is the Normal variable
: = mean , F = std.dev, e = 2.718 and B = 3.1414.
To graph f( x ) , we take x valued on the horizontal axis and f( x ) values on the vertical axis. The location and shape of the curve depends on the values of : and F . As : changes the curve shifts to the left or to the right. As F changes , the shape changes. It becomes fatter or skinnier. Among the infinite possibilities of : and F values , one particular normal distribution is of special interest. That is a normal distribution with : = 0 and
F = 1.
It is called Standard Normal distribution. It is always denoted by Z
Page 1 of 7 Normal Distribution
For these continuous random variables, there is a correspondence between the Probability and Area. The probability that a continuous random variable, X , takes values in the interval ( a , b ) is equal to the area under the curve between the points a and b. Draw Diagram:
Properties of any Normal distribution 1) Total Probability is one.
P ( Z = any value ) = _____________
Symmetric Property.: P ( Z < - a ) = P ( Z > a ) where a is any... [continues]
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