AP Statistics Flashcards: Parameters for a Binomial Distribution
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
Why is it important to interpret the parameters of a binomial distribution in context?
Interpreting parameters in context is crucial because it translates the numerical results into a meaningful understanding of the real-world situation being modeled.
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Why is it important to interpret the parameters of a binomial distribution in context?
Interpreting parameters in context is crucial because it translates the numerical results into a meaningful understanding of the real-world situation being modeled.
For a binomial distribution with a mean of 10 and 50 trials, what is the probability of success (p)?
Since the mean is np, we have 10 = 50 * p. Solving for p gives p = 10/50 = 0.2.
A fair coin is flipped 100 times. What is the mean number of heads?
The mean is np = 100 * 0.5 = 50. We would expect to get 50 heads on average.
What are the two primary parameters used to define a specific binomial distribution?
The two parameters for a binomial distribution are 'n', the fixed number of trials, and 'p', the probability of success on each trial.
What is the formula for the mean of a binomial random variable?
The mean of a binomial random variable is calculated using the formula μ = np, where 'n' is the number of trials and 'p' is the probability of success.
If 10% of products from a factory are defective, what is the standard deviation for the number of defects in a random sample of 400 products?
The standard deviation is sqrt(np(1-p)) = sqrt(400 * 0.1 * 0.9) = sqrt(36) = 6.
What do the mean and standard deviation represent for a binomial distribution?
The mean (np) represents the expected number of successes in the long run, while the standard deviation measures the typical variability of the number of successes from the mean.
What is the formula for the standard deviation of a binomial random variable?
The standard deviation of a binomial random variable is calculated using the formula σ = sqrt(np(1-p)).
How do you calculate the parameters for a binomial distribution?
The parameters 'n' (number of trials) and 'p' (probability of success) are typically identified from the problem's context, while the mean (np) and standard deviation (sqrt(np(1-p))) are calculated from them.
A basketball player makes 80% of their free throws. If they attempt 20 free throws in a game, what is the expected number of successful shots?
The expected number of successful shots is the mean, calculated as np = 20 * 0.80 = 16.