Binomial Distribution
Definition
In statistics, a binomial distribution represents discrete data from repeated independent experiments with two possible outcomes (success or failure) and a fixed number of trials. It provides probabilities for each possible number of successes in those trials.
Analogy
Think about flipping a fair coin multiple times. A binomial distribution would help us calculate the probabilities of getting a certain number of heads (successes) out of those flips.
Related terms
Bernoulli Trial: A Bernoulli trial is an experiment with two possible outcomes, usually referred to as success and failure.
Probability Mass Function: The probability mass function (PMF) gives the probability that a discrete random variable takes on a specific value.
Expected Value: The expected value is the average outcome of a random variable over many trials. It represents the long-term average result.
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Practice Questions (13)
In a binomial distribution, the probability of success for each trial is 0.3. What is the probability of failure for each trial?
Which type of variable is used in binomial distribution?
What is the binomial distribution formula, where n is the number of trials, x is the number of successes, and p is the probability of success?
In a binomial distribution, the probability of success for each trial is 0.25. What is the probability of getting at least 2 successes in 5 independent trials?
Which of the following conditions is necessary for using the binomial distribution to model a random event?
Which condition is not required for using the binomial distribution to model a random event?
Which of the following is a necessary condition for using the binomial distribution?
In a binomial distribution, if the probability of success on each trial increases, what happens to the standard deviation?
In a binomial distribution, what happens to the mean as the number of trials increases?
If a random event does not meet one of the conditions for using the binomial distribution, what does it indicate?
What must be true about the probability of success in order to use a binomial distribution?
How should trials be conducted in order to use a binomial distribution?
Which is a mnemonic device to help remember the conditions of a binomial distribution?
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