Normal Approximation To The Binomial. To approximate the probability that more than 80 people will contract the disease it is customary to compute PXgt 805. For n to be sufficiently large it. Use the normal approximation to the binomial to find the probabilities for the specific value s of X. Assume you have a fair coin and wish to know the probability that you would get 8 heads out of 10 flips.
Lets begin with an example. This is known as the normal approximation to the binomial. You must meet the conditions for a binomial distribution. Use the normal approximation to the binomial to find the probabilities for the specific value s of X. As usual well use an example to motivate the material. The general rule of thumb to use normal approximation to binomial distribution is that the sample size n is sufficiently large if np 5 and n1 p 5.
The Central Limit Theorem is the tool that allows us to do so.
Here we want to determine when the normal approximation is most useful to use when approximating the binomial distribution. He later appended the derivation of his approximation to the solution of a problem asking for the calculation of an expected value for a. By the way you might find it interesting to note that the approximate normal probability is quite close to the exact binomial probability. That is Z X μ σ X np np 1 p N0 1. Using the normal approximation to the binomial distribution simplified the process. The number of trials n is large.