Question

Large Counts condition To use a Normal distribution to approximate binomial probabilities, why do we require that both $np$and $n(1-p)$ be a t least $10$?

Short answer

the shape of binomial distribution to normal distribution n p and n p 10 is used.

Step-by-step solution

Given Informaiton

check $np$and $np\ge 10$to use the normal approximation to binomial probabilities.

Simplification

whether to use the normal approximation to binomial probabilities $np$and $np\ge 10$because there is a significant variation in the form of the binomial and normal distributions. Thus, in order to transform the shape of a binomial distribution to that of a normal distribution, n p and $np\ge 10$is used.