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What is the formula for the mean (expected value) of a binomial distribution?
$E(X) = n * p$
What is the formula for the standard deviation of a binomial distribution?
$ฯ_x = \sqrt{n * p * (1-p)}$
What is the formula for the 10% condition?
n < 0.10N, where n is the sample size and N is the population size.
Define Binomial Distribution.
Probability distribution of the number of successes in a sequence of independent trials, each with a binary outcome.
Define 'success' in a binomial setting.
The desired outcome in a trial of a binomial experiment.
Define 'trial' in a binomial setting.
One instance of performing the experiment.
Define the 10% condition.
When sampling without replacement, ensure the sample size (n) is less than 10% of the population size (N): n < 0.10N.
Define 'n' in a binomial distribution.
The number of trials in the experiment.
Define 'p' in a binomial distribution.
The probability of success on a single trial.
What are the differences between the conditions when sampling with and without replacement?
With replacement: Trials are always independent. | Without replacement: Check the 10% condition (n < 0.10N) to approximate independence.
What are the differences between mean and standard deviation?
Mean: Average number of successes expected. | Standard Deviation: Typical variation of the number of successes from the mean.