Question

What is binomial distribution table ?

Answer 1

Step-by-step explanation:

A binomial distribution table is a table that lists the probabilities of obtaining a specific number of success outcomes in a fixed number of independent trials, given a constant probability of success in each trial. The binomial distribution is a discrete probability distribution that describes the number of success outcomes in a fixed number of independent trials with a binary outcome (success or failure).

The table lists the probabilities of obtaining k successes in n trials, where k is a non-negative integer and n is a positive integer. The probabilities are calculated using the binomial formula, which is given by:

P(k successes in n trials) = (n choose k) * p^k * (1 - p)^(n-k)

where (n choose k) is the number of ways to choose k success outcomes from n trials, p is the probability of success in each trial, and (1 - p) is the probability of failure in each trial.

Binomial distribution tables are useful for solving problems related to counting and probability, especially in situations where the number of trials is fixed and the probability of success is constant. They can also be used for hypothesis testing, calculating confidence intervals, and estimating population proportions in statistical applications.

Answer 2

A binomial distribution table helps calculate the probability of obtaining a specific number of successes in a fixed number of independent Bernoulli trials, with a known probability of success. It is a fundamental tool in statistics, represented by the notation X ~ B(n, p), where n is the number of trials and p is the probability of success per trial.

Step-by-step explanation:

A binomial distribution table is a tool used in statistics to determine the probability of a specific number of successes in a fixed number of independent trials, where each trial has two possible outcomes. In the context of a binomial distribution, trials are known as Bernoulli trials, and they must all be conducted under the same conditions with the outcomes being independent of each other. The table lists the probabilities associated with obtaining various numbers of successes in a series of trials, and can be denoted as X ~ B(n, p), where X is a random variable, n represents the total number of trials, and p is the probability of success in each trial.

The mean (or expected value) for a binomial distribution is given by μ = np, and the standard deviation is given by σ = √npq, where q is the probability of failure (q = 1 - p). The binomial probability distribution function helps us calculate the probability of getting exactly x successes in n trials, which is expressed as P(X = x).

As the number of trials n becomes large and the probability p becomes small, the binomial distribution can be approximated by the Poisson distribution. For practical purposes, when calculations involve a high number of trials, the normal approximation to the binomial distribution is also used, especially before the widespread availability of computers and software capable of computing exact probabilities.