What Normal approximation is
Normal approximation is a method used to approximate the binomial distribution. It is used when the number of trials is large, the probability of success is not too close to 0 or 1, and the number of successes is not too close to the total number of trials.
The steps for normal approximation are as follows:
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Determine the mean of the binomial distribution, based on the total number of trials and the probability of success.
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Determine the standard deviation of the binomial distribution, based on the total number of trials and the probability of success.
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Approximate the binomial distribution with a normal distribution using the mean and standard deviation determined in steps 1 and 2.
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Calculate the probability of the desired outcome using the normal distribution.
Examples
- Estimating the probability of getting a particular value in a single draw from a normal distribution.
- Estimating a population mean from a sample mean when the population standard deviation is known.
- Testing a hypothesis about a population mean when the population standard deviation is known.
- Predicting the probability of a binomial random variable being equal to or greater than a particular value.
- Testing the validity of a model by comparing the observed data to a normal distribution.