The binomial distribution is used to calculate probabilities when a trial with two outcomes is repeated ‘n’ number of times. The expected value tells us the average value we expect to get when the trial is repeated many times. The standard deviation tells us how much variation we expect in the value taken by the random variable. The random variable stays within 3 standard deviations of the mean 99% of the time.
σ = 3.131
To understand how to calculate the mean and variance of a binomial random variable manually click here.
