Characterizing Uncertainty -A Discussion Responses

Description

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?

Dave Pearlman

  1. What is a confidence level and when do we use it?
  2. Can we identify a distribution as a binomial distribution if only 3 of the 4 factors are present? Why or why not?
  3. How does probability support confidence level and vice versa? Explain your answer.

Be constructive and professional.

1)a) The value is not exactly known, however hovers around a certain magnitude.  

b) A discrete random variable is finite and countable. It is a value that can be known specifically and accurately. For example, the cars entering the workshop can be counted so this is a discrete random variable – 1,2,3,4,…..cars in a day. A continuous variable would be just the opposite, one that cannot be counted; for example the time it takes to repair the vehicles.

2)a)

p (probability of success) is constant in the n tests carried out

q (probability of failure) is constant in the n tests carried out and equal to q=1-p

The results obtained can be of two types: p or q, that is, success or failure

Independent of results obtained

b) If we can use the data, it must be determined if there are two results – success or failure – 

Dates of binomial distribution in Excel are.

Exit number = n

Essays = 15p = 0.95

accumulate = 0

P(q) = 1 – P(p)

P(p) = 0.0133

P(q) = 1 -0.0133 = 0.9867

Reply

Lauren Saenz

  1. What is a confidence level and when do we use it?
  2. Can we identify a distribution as a binomial distribution if only 3 of the 4 factors are present? Why or why not?
  3. How does probability support confidence level and vice versa? Explain your answer.

Be constructive and professional.

A random variable is a variable whose value is not exactly known, but is known to be around a certain size. For me personal to differentiate a discrete from a continuous random variable is by knowing a discrete random variable is finite and a countable number where its value can be accurately known in the example of cars entering the business workshop. Since these can physically be counted i.e. 1,2,3,4, etc. Basically, we are able to physically count everyone going in where as a continuous variable is something that we cannot count. For example, for cases in the repair time, the repair time is always random. Sometimes a repair can be done in 5 minutes, 3 hours or a week.

When it comes to binomial experiment there are four characteristics. First is the number of observations n is fixed. Second, each observation is independent. Three, each observation represents two outcomes (success or failure) and lastly, four, the probability of the “success” p is the same for each outcome. The binomial model can be used for this process since we must determine between two possible results which would be success or failure. If all of the conditions are satisfied then the experiment consist of n similar trials and the results in one of the two outcomes being success and/or failure, the probability of success “p” remains the same from trail to trail and n trails are considered independent – the outcome of any trail doesn’t affect the comes of others.

Dates of binomial distribution in Excel are.

Exit number = n

Essays = 15p = 0.95

accumulate = 0

P(q) = 1 – P(p)

P(p) = 0.0133

P(q) = 1 -0.0133 = 0.9867

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