Normal Approximation to Binomial Distribution
Let X be a binomially distributed random variable with number of trials n and probability of success p.
The mean of X is μ=E(X)=np and variance of X is σ2=V(X)=np(1−p).
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 n(1−p)≥5.
For sufficiently large n, X∼N(μ,σ2). That is Z=X−μσ=X−np√np(1−p)∼N(0,1).
Normal Approx. to Binomial Distribution | ||
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No. of Trials (n) | ||
Probability of Success (p) | ||
Select an Option | ||
Enter the value(s) : |
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Results | ||
Mean (μ=np) | ||
Standard deviation (√np(1−p)) | ||
Required Probability : |
Formula
- P(X=A)=P(A−0.5<X<A+0.5)
- P(X<A)=P(X<A−0.5)
- P(X≤A)=P(X<A+0.5)
- P(A<X≤B)=P(A−0.5<X<B+0.5)
- P(A≤X<B)=P(A−0.5<X<B−0.5)
- P(A≤X≤B)=P(A−0.5<X<B+0.5)