Binomial Distribution

Flashcard
•
Mathematics
•
11th - 12th Grade
•
Hard
+3
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a binomial distribution?
Back
A binomial distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent states and is characterized by the number of trials, the probability of success, and the number of successes.
Tags
CCSS.HSS.MD.A.3
CCSS.HSS.MD.A.4
2.
FLASHCARD QUESTION
Front
What are the parameters of a binomial distribution?
Back
The parameters of a binomial distribution are n (the number of trials) and p (the probability of success on each trial).
Tags
CCSS.HSS.MD.A.3
CCSS.HSS.MD.A.4
3.
FLASHCARD QUESTION
Front
How do you calculate the probability of exactly k successes in a binomial distribution?
Back
The probability of exactly k successes in a binomial distribution can be calculated using the formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where (n choose k) = n! / (k!(n-k)!).
Tags
CCSS.HSS.MD.A.3
CCSS.HSS.MD.A.4
4.
FLASHCARD QUESTION
Front
What is the formula for calculating 'n choose k'?
Back
The formula for 'n choose k' is: (n choose k) = n! / (k!(n-k)!), where n! is the factorial of n.
5.
FLASHCARD QUESTION
Front
What does it mean to find the probability of 'at least k' successes?
Back
Finding the probability of 'at least k' successes means calculating the probability of k or more successes occurring in a given number of trials.
Tags
CCSS.HSS.MD.A.2
6.
FLASHCARD QUESTION
Front
How do you calculate the probability of at least k successes in a binomial distribution?
Back
To calculate the probability of at least k successes, you can use the complement rule: P(X >= k) = 1 - P(X < k) = 1 - Σ P(X = i) for i = 0 to k-1.
Tags
CCSS.HSS.MD.A.2
7.
FLASHCARD QUESTION
Front
What is the expected value of a binomial distribution?
Back
The expected value (mean) of a binomial distribution is given by the formula: E(X) = n * p.
Tags
CCSS.HSS.MD.A.2
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