Importance of Normal Distribution
Normal distribution plays a very important role in statistical theory and in particular in sampling theory. It has been found that:
a.Data obtained from psychological physical and biological measurements approximately follow normal distribution .I. Q scores heights and weights of individuals diameters of machines parts lengths of tobacco leaves are example of measurements which are normally distributed or nearly no.
b. Distribution like binomial Poisson etc can be approximated to normal distribution,
If the number of trials nis indefinitely large and neither p nor q is very small than binomial distribution tends of normal distribution.
If the parameter m is indefinitely large ( i, e, if m ) then Poisson distribution tends to normal distribution.
c.For large samples any statistic ( i ,e, sample mean s, d, etc) approximately follows normal distribution and such it can be studied with the help of normal curve.
d.Normal curve is used to find confidence limits of the population parameters.
e.Normal distribution are largely applied in statistical quality control in industry for finding control limits.
f.The theory of errors of observation in physical measurements is based on normal distribution.