Binomial Distribution
Flashcard
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
+1
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What are the assumptions of the Binomial distribution?
Back
1. There are a fixed number of trials. 2. Each trial has two possible outcomes (success or failure). 3. The probability of success is constant for each trial. 4. The trials are independent.
2.
FLASHCARD QUESTION
Front
What is the formula for calculating the probability of exactly k successes in n trials in a Binomial distribution?
Back
P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where p is the probability of success.
Tags
CCSS.HSS.MD.A.3
CCSS.HSS.MD.A.4
3.
FLASHCARD QUESTION
Front
What does 'n choose k' represent in the Binomial formula?
Back
'n choose k' (denoted as C(n, k) or nCk) represents the number of ways to choose k successes from n trials.
Tags
CCSS.HSS.MD.A.2
4.
FLASHCARD QUESTION
Front
How do you calculate the probability of at least k successes in a Binomial distribution?
Back
P(X ≥ k) = 1 - P(X < k) = 1 - Σ P(X = i) for i = 0 to k-1.
Tags
CCSS.HSS.MD.A.2
5.
FLASHCARD QUESTION
Front
What is the mean (expected value) of a Binomial distribution?
Back
The mean is given by μ = n * p, where n is the number of trials and p is the probability of success.
Tags
CCSS.HSS.ID.A.4
6.
FLASHCARD QUESTION
Front
What is the variance of a Binomial distribution?
Back
The variance is given by σ² = n * p * (1 - p), where n is the number of trials and p is the probability of success.
7.
FLASHCARD QUESTION
Front
What is the standard deviation of a Binomial distribution?
Back
The standard deviation is given by σ = √(n * p * (1 - p)).
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