What are the 4 requirements for binomial distribution?

The four requirements are:

• each observation falls into one of two categories called a success or failure.
• there is a fixed number of observations.
• the observations are all independent.
• the probability of success (p) for each observation is the same – equally likely.

What are the conditions of binomial distribution explain show with examples?

The binomial is a type of distribution that has two possible outcomes (the prefix “bi” means two, or twice). For example, a coin toss has only two possible outcomes: heads or tails and taking a test could have two possible outcomes: pass or fail. A Binomial Distribution shows either (S)uccess or (F)ailure.

What is the condition the binomial distribution to be symmetrical?

The shape of a binomial distribution is symmetrical when p=0.5 or when n is large.

Under what conditions is a binomial distribution symmetric?

Which of the following conditions must be true for a random variable to follow a binomial distribution?

For a variable to be a binomial random variable, ALL of the following conditions must be met: There are a fixed number of trials (a fixed sample size). The probability of occurrence (or not) is the same on each trial. Trials are independent of one another.

Under what conditions is a binomial distribution skewed right?

When p = 0.5, the distribution is symmetric around the mean. When p > 0.5, the distribution is skewed to the left. When p < 0.5, the distribution is skewed to the right.

Which of the following are criteria for a binomial probability experiment?

Criteria for a Binomial Probability Experiment A fixed number of trials. Each trial is independent of the others. There are only two outcomes. The probability of each outcome remains constant from trial to trial.

Under what conditions can we approximate binomial and Poisson distributions to a normal distribution?

The normal distribution can be used as an approximation to the binomial distribution, under certain circumstances, namely: If X ~ B(n, p) and if n is large and/or p is close to ½, then X is approximately N(np, npq)