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(1p).

The general rule of thumb to use normal approximation to binomial distribution is that the sample size n is sufficiently large if np5 and n(1p)5.

For sufficiently large n, XN(μ,σ2). That is Z=Xμσ=Xnpnp(1p)N(0,1).

Normal Approx. to Binomial Distribution
No. of Trials (n)
Probability of Success (p)
Select an Option
Enter the value(s) :


Results
Mean (μ=np)
Standard deviation (np(1p))
Required Probability :

Formula

  • P(X=A)=P(A0.5<X<A+0.5)
  • P(X<A)=P(X<A0.5)
  • P(XA)=P(X<A+0.5)
  • P(A<XB)=P(A0.5<X<B+0.5)
  • P(AX<B)=P(A0.5<X<B0.5)
  • P(AXB)=P(A0.5<X<B+0.5)