- Use normal probability distribution to calculate binomial probabilities
- Check the conditions for applying a normal distribution to approximate a binomial distribution
Connection Between Binomial and Normal Distributions
Oftentimes, it is adequate to use the mean and standard deviation to describe the most likely values for the number of successes. For large [latex]n~(\mbox{when}~np\geq 10 \mbox{ and } n(1 – p) \geq 10)[/latex], the binomial distribution has an approximate bell shape. So, we can use the normal distribution to approximate the binomial distribution and conclude that nearly all possibilities for the number of successes fall between the mean and [latex]±3[/latex] standard deviations.