Normal Distribution with Binomial Theorem

Even though, the normal is continuous, the binomial is discrete, the two are very similar. We can use the normal distribution to approximate the binomial distribution

What conditions allow us to use the normal for binomial?

1. Mean = np > 5
2. nq > 5 variance = npq. but np > 5 Pretty much, the distribution is not skewed. ^ Example of a distribution skewed left

Since, the distribution its based off is discrete, there are a few points in the continuous probability distribution that will round up to be the same. those points, we must use.

New z-scores

$z=\frac{x-np}{\sqrt{npq}}$

Area from given Interval.

Now that we have the interval, lets say 4.5 < x < 5.5, we find the probability like how we would Normal Distributions with z-score area. so, P(x<5.5) - P(x<4.5)

2<x<3 2.5 = x