Solve the below:
Q: 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:
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).
Number of defective items in a random sample of 15 items
# of defectives Probability
0 0.2059
1 0.3432
2 0.2669
3 0.1285
4 0.0428
5 0.0105
6 0.0019
7 0.0003
8 0.0000
9 0.0000
10 0.0000
11 0.0000
12 0.0000
13 0.0000
14 0.0000
15 0.0000