If our actually observed data do not match the data expected on the basis of assumptions, we would have serious doubts about our assumptions. Such data of assumption often lead to theoretical frequency distributions also known as probability distribution. This distribution is not based on actual experimental data but on certain theoretical considerations. This may be simple two valued distribution like 3:1 as in Mendelian cross or it may be more complicated. Some of the most important probability distributions are,
Binomial and Poisson distribution apply to the discontinuous random variables and are together known as discontinuous distributions. Normal distribution applies to continuous random variables and is called as continuous distribution.
Normal distribution is also known as normal probability distribution which is very useful for continuous random variables. Many statistical data concerned with business and economic problems are displayed in the form of normal distribution. Normal distribution is the cornerstone of the modern biostatistics. It is important for the reason that it plays a vital role in the theoretical and applied statistics.
In many natural processes, random variation matches to a particular probability distribution which is known as the normal distribution. In 1733, English mathematicians deMoivre and Laplace first discovered normal distribution. Later in 1812, German mathematician Gauss rediscovered it to analyze astronomical data, and it consequently became to be known as the Gaussian distribution.
A continuous random variable x is said to have random distribution with parameters of mean (μ) and standard deviation (σ2) if its density function is,
Here,
e and π are mathematical constants
μ is mean
σ is standard deviation
If μ=0 and σ=1 then the variate is called as standard normal variate
Normal probability curve is the curve representing the normal distribution. Normal probability curve is balanced or symmetrical at the mean (m), bell-shaped and the two tails on the right and left sides of the mean extends to the infinity. The shape of the curve is shown in the following figure.
A normal distribution is important statistical data distribution pattern occurring in many natural phenomena, such as height, blood pressure, lengths of objects produced by machines, etc.
Mean=median=mode
Area under μ + σ is 68.27%
Area under μ + 2σd is 95.45%
Area under μ + 3σ is 99.73%
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