# Continuity Correction Calculator (Normal to Binomial)

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The continuity correction calculator finds the probabilities for a binomial distribution by approximating it using the normal distribution.

The continuity correction factor is the change we make in the value of the binomial variable by adding or subtracting 0.5 in order to calculate probabilities using the normal distribution.

Exact binomial probabilities:

P(X = 4): 0.20508

P(X ≤ 4): 0.37695

P(X < 4): 0.17188

P(X ≥ 4): 0.82813

P(X > 4): 0.62305

Approximate probabilities using continuity correction:

P(3.5 < X < 4.5): 0.20452

P(X < 4.5): 0.37591

P(X < 3.5): 0.17139

P(X > 3.5): 0.82861

P(X > 4.5): 0.62409

The rules for the correction factor are:

1. P(X=n) gets replaced with P(n-0.5<X<n+0.5)
2. P(X<n) or P(X≤n) gets replaced with P(X<n+0.5)
3. P(X>n)or P(X ≥n) gets replaced with P(X>n-0.5)

The continuity correction factor can be applied when,

1. The number of trials ‘n’ is large. (Generally, values of n greater than 30 are considered to be large)
2. The probability of success ‘p’ in a trial is sufficiently small.
3. The mean ‘np’ is a finite number.

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