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The Normal Approximation To The Binomial Distribution. Note that this can be done under the following conditions. Normal approximation to the binimial distribution. 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. 5 and 15 heads for a normal distribution with mean 8 and standard deviation 4.
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. Approximating the Binomial distribution Now we are ready to approximate the binomial distribution using the normal curve and using the continuity correction. One can easily verify that the mean for a single binomial trial where S uccess is scored as 1 and F ailure is scored as 0 is p. He later appended the derivation of his approximation to the solution of a problem asking for the calculation of an expected value for a particular game. There are twomajor reasons to employ such a correction. For n to be sufficiently large it needs to meet the following criteria.
Where p is the probability of S.
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. Each experiment can have only two outcomes. The outcome of each trial must be independent. It turns out that if n is sufficiently large then we can actually use the normal distribution to approximate the probabilities related to the binomial distribution. µ np and σ np 1 p. So this is a pretty good approximationThe normal approximation to the binomial distribution tends toperform poorly when estimating the probability of a small range ofcounts.