Applications of The Normal Distribution

Since the standard normal distribution (s.n.d.) is so well tabulated, it is often very useful to approximate other distributions by the s.n.d. This can be done if the mean and variance are known, and if the size of the sample is large enough. This is particularly useful for the case of binomial distributions.

An example is the binomial distribution (in blue) with p=0.35 and N=10 versus the associated normal shown below (in red).

Thought Questions
  1. Since the normal distribution has an infinite range, and the binomial distribution is finite, what happens for large deviations about the mean?
  2. How can we approximate a non-symmetric distribution (binomial with p different from q) by a symmetric distribution? (normal distribution is always symmetric about the mean...)