Question

When dealing with the number of occurrences of an event over a specified interval of time or space, the appropriate probability distribution is a
a. Poisson distribution.
b. Hypergeometric probability distribution.
c. Normal distribution.
d. Binomial distribution.

Answer 1

Answer:

a)  Poisson distribution

use a  Poisson distribution model when events happen at a constant rate over time or space.

Step-by-step explanation:

Poisson distribution

• Counts based on events in disjoint intervals of time or space produce a Poisson random variable.

• A Poisson random variable has one parameter, its mean λ

• The Poisson model uses a Poisson random variable to describe counts in data.

use a  Poisson distribution model when events happen at a constant rate over time or space.

Hyper geometric probability distribution:-

The Hyper geometric probability distribution is a discrete probability distribution that describes the probability of successes (random draws for which the object drawn has a specified feature) in draws without replacement, from a finite population of size that contains exactly objects with that feature where in each draw is either a success or failure.

This is more than geometric function so it is called the Hyper geometric probability distribution

Binomial distribution

• The number of successes in 'n' Bernoulli trials produces a Binomial distribution . The parameters are size 'n' success 'p' and failure 'q'
• The binomial model uses a binomial random variable to describe counts of success observed for a real phenomenon.

Finally use a Binomial distribution when you recognize distinct Bernoulli trials.

Normal distribution:-

• normal distribution is a continuous distribution in which the variate can take all values within a range.

• Examples of continuous distribution are the heights of persons ,the speed of a vehicle., and so on

• Associate normal models with bell shaped distribution of data and the empirical rule.

• connect Normal distribution to sums of like sized effects with central limit theorem

• use histograms and normal quantile plots to judge whether the data match the assumptions of a normal model.

Conclusion:-

Given data use a  Poisson distribution model when events happen at a constant rate over time or space.