What is the formula for a Normal Approximation to the Binomial?
X~Bin(n,p)
X~N(np,npq)
X~U(a,b)
What is the formula for the Normal Approximation to the Poisson?
X~N(λ,λ)
X~Po(λ)
X~N(μ,σ^2)
A Continuity Correction must be used with both Binomial and Poisson.
When doing Continuity Corrections, standardising is not important.
For a Continuity Correction for a Normal Approx. to the Binomial, n must be greater than 50 30 100( 50, 30, 100 ) and p must be between 0.01 and 0.09 0.05 and 0.15 0.1 and 0.9( 0.01 and 0.09, 0.05 and 0.15, 0.1 and 0.9 )
Examples of standardising for Binomial: P(7≤X≥9) → P(❌) P(5<X>8) → P(❌)
What must both values equal for a Continuity Correction for the Normal Approx. to the Poisson?
λ
n
μ
Examples of standardising for the Poisson: P(X<34) → P(X❌) P(X❌) → P(X>40.5) P(X=38) → P(❌) P(X❌) → P(X<64.5) P(X≥25) → P(X❌)
