How do you know when to use binomial or Poisson?

The binomial distribution counts discrete occurrences among discrete trials. The poisson distribution counts discrete occurrences among a continuous domain. Ideally speaking, the poisson should only be used when success could occur at any point in a domain.

Why and under what conditions is the normal distribution usually used as an approximation to the binomial and Poisson Distribution?

Binomial Approximation 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)

What are the conditions for using the Poisson Distribution?

Conditions for Poisson Distribution: Events occur independently. In other words, if an event occurs, it does not affect the probability of another event occurring in the same time period. The rate of occurrence is constant; that is, the rate does not change based on time.

When can a normal distribution be used?

The Empirical Rule for the Normal Distribution You can use it to determine the proportion of the values that fall within a specified number of standard deviations from the mean. For example, in a normal distribution, 68\% of the observations fall within +/- 1 standard deviation from the mean.

When can the normal approximation to the binomial be used?

When n * p and n * q are greater than 5, you can use the normal approximation to the binomial to solve a problem.

Which of the following formulas is used to calculate the mean of a probability distribution?

The formula for the mean of a binomial distribution is μ = nπ.

How do you use the Poisson distribution formula?

The Poisson Distribution formula is: P(x; μ) = (e-μ) (μx) / x! Let’s say that that x (as in the prime counting function is a very big number, like x = 10100. If you choose a random number that’s less than or equal to x, the probability of that number being prime is about 0.43 percent.

When would you use exponential distribution?

Exponential distributions are commonly used in calculations of product reliability, or the length of time a product lasts. Let X = amount of time (in minutes) a postal clerk spends with his or her customer. The time is known to have an exponential distribution with the average amount of time equal to four minutes.