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Q. Describe Standard Normal Distribution?
Ans.
The Standard Normal Distribution has a mean of 0 and a standard deviation of 1. The letter Z is often used to refer to a standard normal random variable.
Note that, although many applications in the real world have a normal distribution, rarely does anything in the real world follow a standard normal distribution. This is a convenient distribution that can be used (after some transformations) for ANY normal distribution. In the following examples, we will work through finding probabilities for a standard normal random variable.
Click here to see a table with probabilities for the standard normal distribution.
The area under the curve, the shaded area in this diagram, represents the probability of a normally distributed random variable obtaining a value less than z,.
The entries in the table are the probabilities that a random variable having the standard normal distribution assumes a value less than z.
f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
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