18. 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.

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

b. 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?

19.

A personnel manager of a large manufacturing plant is investigating the number of reported on-the-job accidents at the facility over the past several years. Let X be the number of such accidents reported during a one-month period. Based on past records, the manager has established the probability distribution for X as shown in the file P04_19.xlsx.

a. Use simulation to generate 1000 values of this random variable X.

b. Is the simulated distribution indicative of the given probability distribution? Explain why or why not.

21. The probability distribution of X, the number of customers in line (including the one being served, if any) at a checkout counter in a department store, is given by P(X = 0) = 0.25, P(X = 1) = 0.25, P(X = 2) = 0.20, P(X = 3) = 0.20, and P(X = 4) = 0.10.

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

b. Is the simulated distribution indicative of the given probability distribution? Explain why or why not.

c. 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?

d. Repeat parts a through c with 5000 simulated values rather than 500. Explain any differences you observe.