When circuit boards used in the manufacture of compact disc players are tested, it is discovered that each has a 5% chance of being defective. Suppose that a batch of 25 of these circuit boards is randomly selected.
Would this be binomial or poission distribution?
Binomial
To determine whether this situation follows a binomial or Poisson distribution, we need to consider the characteristics of each distribution.
A binomial distribution is used when there are a fixed number of trials (in this case, 25 circuit boards) and each trial has only two possible outcomes (defective or not defective). Additionally, the probability of success (being defective) remains constant throughout the trials.
A Poisson distribution, on the other hand, is used when we are dealing with the number of events that occur within a fixed interval of time or space. The events must occur randomly and independently, and the average number of events must be known.
In this scenario, we have a fixed number of 25 circuit boards being tested, and each board can be either defective or not defective (two possible outcomes). However, the given information states that each board has a 5% chance of being defective, which implies that the probability of success (being defective) is not constant throughout the trials. Therefore, it does not satisfy the requirements for a binomial distribution.
Since the Poisson distribution is not applicable either (as it deals with events occurring in a fixed interval), we cannot directly model this scenario using either distribution.