16
Mar
Normal Approximation Of Binomial. For sufficiently large n X Nμ σ2. We showed that the approximate probability is 00549 whereas the following calculation shows that the exact probability using the binomial. Note that this can be done under the following conditions. As the title of this page suggests we will now focus on using the normal distribution to approximate binomial probabilities.
Generally values of n greater than 30 are considered to be large. PX A. Let us illustrate the normal approximation to the binomial by supposing that a particular company has a history of making errors in 10 of its invoices. 281 - Normal Approximation to Binomial. When this is the case we can use the normal curve to estimate the various probabilities associated with that binomial distribution. Note that the normal approximation computes the area between 55 and 65 since the probability of getting a value of exactly 6 in a continuous distribution is nil.
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.
By the way you might find it interesting to note that the approximate normal probability is quite close to the exact binomial probability. This is known as the normal approximation to the binomial. Thus PX k max mbk maxexp m2 2npq for m not too large. Binomial distribution is a discrete distribution whereas normal distribution is a continuous distribution. Connection between the Binomial distribution Poisson distribution and Normal distribution. Generally values of n greater than 30 are considered to be large.