4.4 - Binomial Distributions (2/18)

Considered for discrete, countable data

  • 2 possible outcomes: success or failure (called a Bernoulli Random Variable)

  • Fixed number of trials, n

  • Outcomes are independent (random sample)

  • Probability(p), remains constant for each trial

Notation: Bin(n,p)

Use random sampling to ensure independence

Mean

  • μ=np\mu=np

Variance

  • σ2=np(1−p)\sigma^2=np\left(1-p\right)

Standard Deviation

  • σ=σ2\sigma=\sqrt{\sigma^2}

Plausible: meaning not unusual

Within 2 standard deviations of the mean

If n is large enough, the binomial distribution “acts” like a normal distribution and will be treated as such as “continuity correction” which is .5