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Normal Approximation Binomial Distribution. 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. There must be a fixed number of trials. Then the binomial can be approximated by the normal distribution with mean mu np and standard deviation sigma sqrtnpq. Example 5 Suppose 35 of all households in Carville have three cars what is the probabil-.
In order to get the best approximation add 05 to x or subtract 05 from x use x 05 or x - 05. Then the binomial can be approximated by the normal distribution with mean mu np and standard deviation sigma sqrtnpq. 5 and 15 heads for a normal distribution with mean 8 and standard deviation 4. This is known as the normal approximation to the binomial. The actual binomial probability is 01094 and the approximation based on the normal distribution is 01059. The binomial distribution is a discrete distribution while the normal distribution is a continuous distribution so we can never count on the normal distribution being an exact replication of the binomial distribution.
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Example 5 Suppose 35 of all households in Carville have three cars what is the probabil-. The approximate normal distribution has parameters corresponding to the mean and standard deviation of the 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. Approximating the Binomial Distribution to the binomial distribution first requires a test to determine if it can be used. That is Z X μ σ X np np 1 p N0 1. Each experiment can have only two outcomes.