Connection Between Binomial and Normal Distributions: Learn It 1

  • Use normal probability distribution to calculate binomial probabilities
  • Check the conditions for applying a normal distribution to approximate a binomial distribution

Binomial Distribution

We defined a binomial experiment as an experiment consisting of a fixed number, [latex]n[/latex], of independent Bernoulli trials that count the number of successes out of [latex]n[/latex] trials. Notice that the number of successes in a binomial experiment is a discrete random variable. The distribution of this random variable is modeled with the binomial distribution.

binomial mean and standard deviation

For a binomial experiment with a probability of success [latex]p[/latex] on [latex]n[/latex] trials, the mean [latex]\mu[/latex] and standard deviation [latex]\sigma[/latex] are defined as follows:

  • The mean of the number of successes is [latex]\mu = np[/latex].
  • The standard deviation of the number of successes is [latex]\sigma = \sqrt{np(1-p)}[/latex].