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Respond to each of the following questions in a minimum of 175 words.
Many business activities generate random data. An example described in the textbook is the servicing of cars at an oil change shop (LO 6-4). Each vehicle 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 vehicle.
We can capture the most relevant characteristics of a random process with a simple probability distribution model. We 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 the demand on a Saturday afternoon. Discuss the following:
A. What is a random variable? (Refer LO 6-1).
B. How would you differentiate a discrete from a continuous random variable? (Refer LO 6-1, LO 7-1).
Scenario. Quick oil change shops need to ensure that a car’s service time is not considered “late” by the customer. Service times are either late or not late. Let X be the number of cars that are late out of the total n=10 cars to be serviced.
Assumptions. (a) Cars arrive independently of each other, and (b) The probability of a late car is consistent. P(car is late) = π = 0.20. Discuss the following:
C1. List the five characteristics of a binomial experiment? (Refer LO 6-4).
C2. Can we use a binomial distribution to model this process? What characteristics pertain?
C3. What is the probability that exactly three of the following n = 10 cars serviced are late (P(X = 3))? Use Excel’s = BINOMDIST() function to find the probability.
C4. What is the probability that three or fewer of the following n = 10 cars serviced are late (P(X ≤ 3))?
Reference
Doane, D., Seward, L. (2019) Applied statistics in business and economics (6th ed). McGraw-