Solved: Probability/Distribution/Simulation

Complete Problem 18 in Chapter 4 on page 159.

A quality inspector picks a sample of 15 items at random from a manufacturing process known to produce 10% defective items. Let X be the number of defective items found in the random sample of 15 items. Assume that the condition of each item is independent of that of each of the other items in the sample. The probability distribution of X is provided in the file P04_18.xlsx.

Use simulation to generate 500 values of this random variable X.
Calculate the mean and standard deviation of the simulated values. How do they compare to the mean and standard deviation of the given probability distribution? (Albright, 2017, p. 159).
In the discussion area, answer both questions in Parts a and b. Attach the Excel document.

Expert Partial Solution

In this exercise, it is worthwhile to run the simulation for 500 items to generate random values and hence, understand a larger scale of potential outcomes. As Albright (2017) argues, simulation shows not what will happen but rather what might happen. Through this simulation, the quality inspector will be able to make more informed decisions since it will correctly test out the hypothesis that a random sample of 15 items produces 10% defective items. I used RAND () function to generate a sequence of random numbers. Although Excel software keeps on updating these RAND () values, the computed mean and standard deviation change insignificantly…read more

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Solved: Probability/Distribution/Simulation