Data for Normal Distribution

Normal distribution of data is otherwise known as Gaussian distribution. It is a continuous probability distribution which gives a good description of data that gather around the mean. The normal distribution is frequently used to explain, at least approximately, any variable that tends to cluster around the mean(Source: wikipedia). The Normal Probability Distribution is very general in the field of statistics.

Data for Normal Distribution Example Problems

A random variable X whose distribution has the character of a normal curve is called a normal random variable.

Normal Curve :

In graph the random variable X is thought to exist normally distributed by mean μ and standard deviation σ then its probability distribution is



Properties of data for normal distribution:

1. Normal curve is symmetrical about the mean μ.(Source: intmath)

2. Mean is at the central point and divides the area into halves;

3. Entire area under the curve is equal to 1;

4. Standard deviation σ or variance σ2 and mean is used to determine the normal distribution of data.

In a normal distribution, two parameters are needed, namely mean μ and variance σ2.

Data for Normal Distribution curves

Area under the Normal Curve using Integration:

The probability of a continuous normal variable X establish in a particular interval [a, b] is the area under the curve bounded by x = a and x = b then

and the area depends ahead the values of μ and σ.

The Standard data for  Normal Distribution:

If we standardize our normal curve, with a mean of zero and a standard deviation of 1 unit.

If we have the standardized state of μ = 0 and σ = 1, then,

Algebra is widely used in day to day activities watch out for my forthcoming posts on Piecewise Continuous Function and free math tutoring. I am sure they will be helpful.

We can transform all the clarification of any normal random variable X with mean μ and variance σ  to a new set of observations of another normal random variable Z with mean 0 and variance 1 using the following transformation.

Example:

If μ = 1.5 and σ = 0.5/2.5 are the data, then the  normal distribution.

The graph is as follows: