CONTINUOUS RANDOM VARIABLES The random variables that takes on any value in an interval is called a Continuous variable. For Example : ( 1 ) The Heights and W eights of humans ( 2 ) Length of Life of an equipment ( washing machine, bulb, etc ). ( 3 ) Daily Rainfall at a certain point ( 4 ) The Speed of a jetliner ( 5 ) The W eight of a Sumo wrestler ( 6 ) The Time a student takes to complete an exam ( 7 ) The Blood Pressure of patients admitted to a hospital on a day The probability distribution of these continuous random variables are depicted by Smooth curves.

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.

2)

P ( Z = any value ) = _____________

3)

Symmetric Property.: P ( Z < - a ) = P ( Z > a ) where a is any... [continues]

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