Step 2: Determine the continuity correction to apply. Step 1: Verify that the sample size is large enough to use the normal approximation.įirst, we must verify that the following criteria are met:īoth numbers are greater than 5, so we’re safe to use the normal approximation. To calculate the probability of the coin landing on heads less than or equal to 43 times, we can use the following steps: p (probability of success on a given trial) = 0.50.In this situation we have the following values: Suppose we want to know the probability that a coin lands on heads less than or equal to 43 times during 100 flips. Example: Normal Approximation to the Binomial #A binomial distribution has 100 trials how toThe following step-by-step example shows how to use the normal distribution to approximate the binomial distribution. Using Normal Distribution with Continuity Correction The following table shows when you should add or subtract 0.5, based on the type of probability you’re trying to find: Using Binomial Distribution To use the normal distribution to approximate the binomial distribution, we would instead find P(X ≤ 45.5). In simple terms, a continuity correction is the name given to adding or subtracting 0.5 to a discrete x-value.įor example, suppose we would like to find the probability that a coin lands on heads less than or equal to 45 times during 100 flips. However, the normal distribution is a continuous probability distribution while the binomial distribution is a discrete probability distribution, so we must apply a continuity correction when calculating probabilities. When both criteria are met, we can use the normal distribution to answer probability questions related to the binomial distribution. This is known as the normal approximation to the binomial.įor n to be “sufficiently large” it needs to meet the following criteria: 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. If X is a random variable that follows a binomial distribution with n trials and p probability of success on a given trial, then we can calculate the mean (μ) and standard deviation (σ) of X using the following formulas:
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