<P> In probability theory , the central limit theorem ( CLT ) establishes that , in most situations , when independent random variables are added , their properly normalized sum tends toward a normal distribution ( informally a `` bell curve '' ) even if the original variables themselves are not normally distributed . The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions . </P>
<P> In probability theory , the central limit theorem ( CLT ) establishes that , in most situations , when independent random variables are added , their properly normalized sum tends toward a normal distribution ( informally a `` bell curve '' ) even if the original variables themselves are not normally distributed . The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions . </P>
the central limit theorem provides us with information about
the central limit theorem provides us with information about
normal distribution
normal distribution