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.

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.