Hello,

When the sample size is large and the random variables are Bernoulli variables we can use the normal approximation to the binomial distribution for calculation of p-values.However,for small intervals in the distribution,the approximation fails.

Example:If we wanted to calculate the probability of observing 69,70 or 71 smokers amongst a sample of 400 ,the normal approximation prob is 0.04 whereas the binomial is 0.07.

I am trying to understand why this happens.Is it because when the interval is small the distribution becomes more discrete than continuous??