- vc9493

# Normal Approximation to the Binomial Distribution (Year 13)

Updated: Mar 22

Under certain circumstances we can approximate a binomial distribution (Discrete) by a normal distribution (Continuous).

For n large and p close to 0.5, we can approximate as follows

So **μ = np** and **σ² = np(1-p)** for the binomial are used as parameters in the normal.

As the binomial distribution is a discrete distribution, but the normal is a continuous distribution, the approximation can be refined by using a **continuity correction**.

In general,

Consider P(X ≦ 2) on the discrete scale i.e. the area of the blocks for X = 0, 1, 2. However 2 extends up to 2.5 on the continuous scale, so P(X ≦ 2) ≈ P(X ≦ 2.5)

Similarly, P(X = 3) ≈ P(2.5 ≦ X ≦ 3.5)

__Examples__

Recall also that for the normal distribution there is no distinction between < and ≤, > and ≥