Characteristics of a binomial experiment

 

Many business activities generate data that can be thought of as random. An example described in the textbook is the servicing of cars at an oil change shop. Each car entering the shop can be considered an experiment with random outcomes. A variable of interest in this experiment could be the amount of time necessary to service the car. Service time will vary randomly with each car.

We can often capture the most relevant characteristics of a stochastic process with a simple probability distribution model. We can then analyze the model to make predictions and drive decisions. For instance, we could estimate the number of technicians the oil change shop needs to service demand on a Saturday afternoon. Discuss the following:
• What is a random variable?
• How would you differentiate a discrete from a continuous random variable?

A laptop manufacturing company has implemented a 2-step process to test the quality of each production batch. In the first step, a technician randomly selects 15 laptops from the batch and determines whether they meet specifications. The batch is considered acceptable provided no more than 1 laptop fails to meet specifications. Otherwise, the entire batch must be tested in the second step. Historical data shows that 95% of the laptops produced adhere to specifications. Discuss the following:
• What are the 4 characteristics of a binomial experiment?
• Can we use a binomial distribution to model this process?
• What is the probability that the entire batch unnecessarily has to be tested if in fact 95% of its laptops conform to specifications? (Hint: Use Excel’s =BINOMDIST() function to find the probability.)
• What is the probability that the batch is incorrectly accepted if only 75% of its laptops conform to specifications?

Sample Solution

Characteristics of a binomial experiment

A binomial experiment is an experiment where you have a fixed number of independent trials with only two outcomes. For example, the outcome might involve a yes or no answer. There are four characteristics of a binomial experiment: 1) there are a fixed number of trials – think of trials as repetitions of an experiment. The letter n denotes the number of trials. 2) Each observation is independent. 3) There are only two possible outcomes, called “success” and “failure,” for each trial. The letter p denotes the probability of a success on one trail, and q denotes the probability of a failure on one trial. p + q= 1. 4) The n trials are independent and are repeated using identical conditions. Because the n trials are independent, the outcome of one trial does not help in predicting the outcome of another trial.

population found this perplexing due to the cultural belief in “two-spirit” or what can be considered a third gender (Morgensen. 2012). With the colonization of the indigenous population Europeans were able to instill their beliefs about gender and sex, eventually this became a tool in their quest for dominance (Manning, 2019). Additionally it can be suggested that it created the foundation of a hierarchical system in the Americas and the Caribbean society knows toady. In short the institution of gender was the beginnings of colonial power around the world. With the concept of hierarchy forced on the indigenous colonizers were able to justify gendered violence, because of the man over woman ideal. Gendered violence played an important role in the shaping of colonial societies and establishing power and it continued to be a tool of retaining power during post-colonisation and modern day conflict. It is clear that even in modern day society there is a large amount of inequality throughout the world in terms of men’s and women’s opportunities, and unfortunately the inequalities can become amplified during times of conflict. During World War 1 80% of casualties were soldiers, during the Vietnam War 80% of casualties were civilians mostly women and children (Fagan,1999). This is an example of an extremely concerning trend and that is that women and children have become tools and pawns in conflicts to gain or retain power on both international and national levels. As instability in security increases the risk of sexual violence also increases all across the board for men, women, and children. The use of sexual violence is used a psychological tactic to control and weaken communities through loss of social cohesion. Colonization and war both contributed to the objectification and demoralization use of sexual violence to carry out the task at hand. We see this with early colonizers who were quick to brutalize native women and exploit their newly taken power. A more modern examples would be the conflicts in Rwanda, Uganda, and Bosnia–Herzegovina, which saw sexual violence used as a systemic tool of war; but also can be used to control populations in times of peace (Close, 2011). The use of sexual violence reinforces gender stereotypes in societies both developed and developing, especially the idea that conflict is a male dominated.

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