In the context of quality control, which probability distribution is most commonly used to calculate the probability of producing a defect in a single trial?

• A. $Bernoullidistribution$
• B. $Poissondistribution$
• C. $Normaldistribution$
• D. $Binomialdistribution$

Answer: (A)

Verified step by step guidance

1. Understand the context: In quality control, we often want to model the probability of producing a defect in a single trial, which is a scenario with only two possible outcomes — defect or no defect.
2. Recall the Bernoulli distribution: It is a discrete probability distribution for a random variable which takes the value 1 (success, e.g., defect) with probability \(p\) and 0 (failure, e.g., no defect) with probability \$1-p$ in a single trial.
3. Compare with other distributions: The Binomial distribution models the number of successes in multiple independent Bernoulli trials, the Poisson distribution models the number of events in a fixed interval, and the Normal distribution is continuous and used for approximations or measurements with many outcomes.
4. Since the problem focuses on a single trial with two possible outcomes, the Bernoulli distribution is the most appropriate choice to calculate the probability of producing a defect in that single trial.
5. Therefore, identify the Bernoulli distribution as the correct distribution to use for this scenario.