All Flashcards
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 is the formula for the mean (expected value) of a binomial distribution?
What is the formula for the standard deviation of a binomial distribution?
What is the formula for the 10% condition?
n < 0.10N, where n is the sample size and N is the population size.
Explain the concept of independence in the context of binomial trials.
The outcome of one trial does not affect the outcome of any other trial.
Explain the importance of the 'Binary' condition in a binomial setting.
Each trial must have only two possible outcomes: success or failure. This is fundamental to the binomial model.
Explain why the 10% condition is important when sampling without replacement.
It ensures that removing one item from the population doesn't significantly change the probabilities for subsequent draws, allowing us to treat trials as approximately independent.
Explain the meaning of the expected value in a binomial distribution.
It represents the average number of successes you would expect over many repetitions of the experiment.
Explain what 'n' represents in the context of a binomial distribution.
'n' represents the number of independent trials performed in the experiment. This number must be fixed in advance.
Explain what 'p' represents in the context of a binomial distribution.
'p' represents the probability of success on a single trial. This probability must be the same for each trial.