01:960:285 Lecture Notes - Lecture 17: Standard Deviation, Central Limit Theorem, Probability Distribution

• School: Rutgers University
• Department: Statistics and Biostatistic
• Course: 01:960:285
• Professor: Shyam Moondra

Document Summary

Recall that according to the central limit theorem, the sample mean of any distribution will become approximately normal if the sample size is sufficiently large. It turns out that the binomial distribution can be approximated using the normal distribution if np and nq are both at least 5. Furthermore, recall that the mean of a binomial distribution is np and the variance of the binomial distribution is npq. There is a problem with approximating the binomial with the normal. That problem arises because the binomial distribution is a discrete distribution while the normal distribution is a continuous distribution. The basic difference here is that with discrete values, we are talking about heights but no widths, and with the continuous distribution we are talking about both heights and widths. The correction is to either add or subtract 0. 5 of a unit from each discrete x-value. This fills in the gaps to make it continuous.