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.

1. Use simulation to generate 500 values of this random variable X.
2. 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.