The document asks three questions: (1) Why is the normal distribution so important for statistical inference problems? (2) Why is the normal distribution computationally useful, given its wide applicability? (3) In the QM3341 course, why are other distributions introduced when discussing tests like goodness of fit and ANOVA? The response explains that (1) by the central limit theorem, the distribution of a large random sample is normally distributed, making it important for statistical inference. (2) Most practical problems follow normal distributions, making it useful computationally.

1. My question is three-fold:
(a) Why is the Normal distribution so important, particularly with respect to problems dealing
with statistical inference?
(b) Ok, now that we accept/believe that the Normal distribution is so widely applicable,
computationally why is it so useful?
(c) Finally, in QM3341 when we discuss tests like Goodness of Fit, Independence, ANOV, why
are other distributions introduced?
Solution
(a) by central limit theorem distribution function of a random sample of size n taken from an
unknownly distributed population is normally distributed as n tends to infinity .
general assumption n greater than equal to 30 is sufficient to assume normal distribution of a
random sample.
hence, normal distribution so important, particularly with respect to problems dealing with
statistical inference.
(b) Most of the practical problems follow normal distributions.