Question

If the number of surface nonconformities on a specific size of metal piece during one production shift is the discrete random variable in question, then the appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 defectives is given most likely by which distribution?

1) Bernoulli
2) Poisson
3) Defective
4) Both A and B

Answer 1

2) Poisson

The appropriate probability distribution for the given scenario is the Poisson distribution.

Step-by-step explanation:

The appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 defectives is most likely the Poisson distribution.

The Poisson distribution is used to model the probability of a specific number of events occurring in a fixed interval of time or space, given a known average rate and independence of events. In this case, the number of surface nonconformities on a metal piece during one production shift is the discrete random variable, and we want to find the probability of 3 defectives.

This scenario satisfies the requirements for using the Poisson distribution: the number of nonconformities is countable, the average rate of nonconformities is known, and the nonconformities occur independently of each other. Therefore, option 2) Poisson is the most appropriate probability distribution to use.