Binomial Distribution Mixed Review

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: the number of trials (n) and the probability of success (p).

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).

Front

How do you calculate the probability of getting exactly k successes in n trials?

Back

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

Front

What is the difference between binompdf and binomcdf?

Back

binompdf(n, p, k) calculates the probability of getting exactly k successes in n trials, while binomcdf(n, p, k) calculates the cumulative probability of getting k or fewer successes.

Front

How do you find the probability of getting at least k successes?

Back

To find the probability of getting at least k successes, use: P(X >= k) = 1 - binomcdf(n, p, k-1).

Front

How do you find the probability of getting less than k successes?

Back

To find the probability of getting less than k successes, use: P(X < k) = binomcdf(n, p, k-1).

Front

What is the probability of getting at least 2 successes in 10 trials with p = 0.11?

Back

Use: P(X >= 2) = 1 - binomcdf(10, 0.11, 1).

Front

What is the probability of getting exactly 2 correct answers when guessing on 5 multiple choice questions with 4 options each?

Back

Use: P(X = 2) = (5 choose 2) * (0.25)^2 * (0.75)^3 = 0.2636.

Front

What does 'n choose k' mean in binomial probability?

Back

'n choose k' refers to the number of ways to choose k successes from n trials, calculated as n! / (k!(n-k)!).

Front

What is the expected value of a binomial distribution?

Back

The expected value (mean) of a binomial distribution is calculated as E(X) = n * p.