Normal Approximations

This week's and last week's readings have included the Binomial, Poisson, and Normal distributions. Each provides very accurate results when used in the circumstances for which they are intended in quality engineering. However, the Binomial and Poisson distributions can get very cumbersome to calculate as the scale of the sample size grows. The tables of values provided in most textbooks typically don't provide values for very large sample sizes. (The largest sample size supported in our text appendices is 36.) As a result, it is conventional to use the Normal distribution as an approximation of either the Binomial or Poisson distribution as sample sizes grow.

Discuss what it means to use the Normal distribution as an approximation for the Binomial or Poisson distribution. Why does it work? What are the strengths or weaknesses of doing so?(Hint: Think about the center versus the tails.)

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