Question

conceptional question

when the binomial distribution, the n is getting larger then it is closed to normal distribution or standard normal distribution???

I read the textbook and it said after standardize it will close to standard normal distribution, does that mean if i don't standardize, then it will not close to the normal distribution???

Answer 1

if n get larger then the binomial distribution is closed to the normal distribution with its mean and variance.

The selection of the correct normal distribution is determined by the number of trials n in the binomial setting and the constant probability of success p for each of these trials. The normal approximation for our binomial variable is a mean of np and a standard deviation of (np(1 - p))^0.5.

By using some mathematics it can be shown that there are a few conditions that we need to use a normal approximation to the binomial distribution. The number of observations n must be large enough, and the value of p so that both np and n(1 - p) are greater than or equal to 10. This is a rule of thumb, which is guided by statistical practice. The normal approximation can always be used, but if these conditions are not met then the approximation may not be that good of an approximation.