Binomial Distribution

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 defined by two parameters: n (number of trials) and p (probability of success).

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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

Front

How do you calculate the mean of a Binomial Distribution?

Back

The mean (μ) of a Binomial Distribution is calculated using the formula: μ = n * p.

Front

How do you calculate the standard deviation of a Binomial Distribution?

Back

The standard deviation (σ) of a Binomial Distribution is calculated using the formula: σ = √(n * p * (1 - p)).

Front

What is the probability of getting at least one success in a Binomial Distribution?

Back

The probability of getting at least one success is calculated as: P(X ≥ 1) = 1 - P(X = 0), where P(X = 0) is the probability of zero successes.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

What is the formula for calculating the probability of exactly k successes in a Binomial Distribution?

Back

The formula is: P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), where (n choose k) = n! / (k!(n-k)!).

Front

If n = 20 and p = 0.1, what is the probability of getting exactly 2 successes?

Back

Using the formula: P(X = 2) = (20 choose 2) * (0.1)^2 * (0.9)^(20-2) = 0.1937.

Tags

CCSS.HSS.MD.A.2

Front

What does 'at most k successes' mean in a Binomial Distribution?

Back

'At most k successes' means the probability of getting k or fewer successes, calculated as P(X ≤ k).

Front

How do you interpret the standard deviation in a Binomial Distribution?

Back

The standard deviation indicates the variability or spread of the distribution; a larger standard deviation means more variability in the number of successes.

Front

What is the relationship between Binomial Distribution and the Normal Distribution?

Back

For large n, the Binomial Distribution can be approximated by the Normal Distribution, especially when both np and n(1-p) are greater than 5.

Tags

CCSS.HSS.ID.A.4