two percent of mobile phones produced at a factory are defective. which of the following is a binomial…

two percent of mobile phones produced at a factory are defective. which of the following is a binomial experiment? selecting phones randomly until a non - defective phone is chosen selecting phones randomly until 200 defective phones are chosen selecting 200 phones randomly and recording whether each phone is defective selecting a group of phones randomly and recording the number of defective phones in the group

two percent of mobile phones produced at a factory are defective. which of the following is a binomial experiment? selecting phones randomly until a non - defective phone is chosen selecting phones randomly until 200 defective phones are chosen selecting 200 phones randomly and recording whether each phone is defective selecting a group of phones randomly and recording the number of defective phones in the group

Answer

Explanation:

Step1: Recall binomial experiment criteria

A binomial experiment has a fixed - number of trials ($n$), each trial has only two possible outcomes (success or failure), the probability of success ($p$) is constant for each trial, and the trials are independent.

Step2: Analyze each option

  • Option 1: Selecting phones randomly until a non - defective phone is chosen is a geometric experiment, not binomial as the number of trials is not fixed.
  • Option 2: Selecting phones randomly until 200 defective phones are chosen is a negative binomial experiment, not binomial as the number of trials is not fixed.
  • Option 3: Selecting 200 phones randomly and recording whether each phone is defective. Here, $n = 200$ (fixed number of trials), each phone is either defective (success) or non - defective (failure), the probability of a phone being defective ($p=0.02$) is constant for each trial, and the selection of each phone is independent. This is a binomial experiment.
  • Option 4: Selecting a group of phones randomly and recording the number of defective phones in the group. Since the size of the group is not fixed, it is not a binomial experiment.

Answer:

Selecting 200 phones randomly and recording whether each phone is defective