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.