Mean variance and standard deviation of binomial distributions

Learning Objectives Identify the parameters (n and p) of a binomial distribution from a problem description. State and apply the formulas for the mean, variance, and standard deviation of a binomial distribution. Calculate the mean (expected value) of a binomial random variable. Calculate the variance of a binomial random variable. Calculate the standard deviation of a binomial random variable. Interpret the mean and standard deviation in the context of a real-world scenario. Distinguish between variance and standard deviation and understand their relationship. If 80% of students pass a test, how many would you expect to pass in a class of 30, and how much would that number typically vary? 🤔 This tutorial connects our work with functions to the world of statistics. While...

TermDefinitionExample Binomial DistributionA discrete probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure).The number of 'heads' you get when you flip a fair coin 20 times. Here, n=20 and p=0.5. Trial (n)A single performance of a random experiment. In a binomial distribution, 'n' is the total, fixed number of independent trials.In a 10-question multiple-choice quiz, there are 10 trials (n=10). Success (p)The outcome of interest in a trial. 'p' is the constant probability of a success occurring in any single trial.If you are rolling a die and want to get a '6', a 'success' is rolling a 6. The probability of success is p =...

Mean (Expected Value) of a Binomial Distribution \mu = np To find the expected number of successes, multiply the number of trials (n) by the probability of success on a single trial (p). Variance of a Binomial Distribution \sigma^2 = npq To find the variance, multiply the number of trials (n) by the probability of success (p) and the probability of failure (q). Remember that q = 1 - p. Standard Deviation of a Binomial Distribution \sigma = \sqrt{npq} To find the standard deviation, simply take the square root of the variance. This value measures the typical deviation from the mean.