Characterizing Uncertainty

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Respond to the following discussion prompt in a minimum:

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

In most centers, the procedure is approached using antegrade or transvenous method by creating an arteriovenous guide wire loop; which is the standard technique for transcatheter VSD device closure. Some studies have described that retrograde method and transarterial approach cannot be performed due to technical difficulties, mostly in adult patients. Recent studies of using variety of Amplatzer occluder devices had been successful with retrograde technique in adolescents and children with congenital VSD. Retrograde technique involves fewer steps and possesses the potential to significantly reduce fluoroscopy and total procedure time in comparison with the conventional methods. In a case series of Pekel et al. presented their experience of the transcatheter VSD closure using transarterial retrograde approach and concluded that it simplifies the procedure, decreases the radiation exposure, and shortens the procedure time.13 After a thorough literature search, no local study on transcatheter device closure of VSD comparing the two techniques was published.
Early in this institution, most patients with ventricular septal defect that undergo transcatheter technique still use the conventional method (transvenous antegrade approach). Only ten years ago, transcatheter closure using implantable devices has been introduced and is recently gaining popularity. When explaining the therapeutic options to the patients or the parents with VSD, outcome goals and complications or adverse events should be fully discussed. Since transcatheter device closure of VSD is an evolving technology, data on effectiveness, cost and mid-term outcome comparing these two technique

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