Statistical Sciences 2141A/B Lecture 19: Section 5.3

• School: Western University
• Department: Statistical Sciences
• Course: Statistical Sciences 2141A/B
• Professor: Joe Raaymakers

Document Summary

The normal distribution provides a good approximation of the probability values of certain other distributions which can make calculations using the cdf easier. The most common example is the normal approximation of the binomial distribution. Recall that the binomial distribution b(n, p) has expected value and variance n = number of trials. Also recall that although the pmf for the binomial distribution is skewed for values p 0. 5, it is approximately bell-shaped. The probability values for x ~ b(n, p) can be approximated by those of n(np, np(1 - p)) using the following: Note that a continuity correction of 0. 5 is included in the calculations in order to improve the approximation since the binomial is discrete and its pmf increases at each integer. When to use the normal approximation vs poisson"s approximation. Recall that a poisson approximation can be used for a binomial distribution where n is large and p is small (n > 50 and np < 5)