Question
This is a graded discussion: 40 points possible due Sep 22 at 8pm Since this is a gro up discussion, each group has its own conversation for this topic. Here are the ones you have access to: u03d1 - Normal Approximations 127 127 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 text books 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? Response Guideline Post your response of 1-3 paragraphs (about 100-200 words) by the due date for this discussion assignment, and then reply to at least two initial responses of your peers during the remainder of the week, particularly focusing on responses that might differ from your own. Also respond appropriately to anyone who posts questions against your own postings. Discuss the content! Keep responses focused on the substance of the issue, not simply on agreeing with a comment or encouraging each other. Search entries or author Unread Reply
Explanation / Answer
The normal approximation to binomial ad poission is very useful in the cases where p = 0.5 or very close to 0.5.
But in cases where p deviates very much from this symmetric value of 0.5, the resulting binomial distribution is highly skewed, and in this case the symmetric normal distribution can not be used to approximate the skewed binomial.
However in cases where binomial is indeed symmetric or very close to symmetric, normal approximation is a good choice in cases of large sample sizes because it also gives the advantage of contiuity correction, which is absent in the discrete binomial distribution.
Hope this helps !
