In a factory, plastics is produced in volumetric chunks. The number of chunks produced daily is a discrete Binomial random variable with parameters n = 50 and p = 0.62. The weight of material per chunk is a continuous random variable in tons with the following probability density function:
| 00.070.02(x x 4)2 + 0.22f(x) =0.08(5 x) + 0.20 0.04x + 0.32 | x < 0 0 x 22 < x 55 < x 7 7 < x 8if x > 8 |
- Conduct a Monte Carlo study to estimate the probability that the total weight of the plastics produced by the factory in a week of five workdays exceeds 640 tons, which constitutes a violation of regulations in place. Use 5n and p as the required distribution parameters. With probability 0.98, your answer should differ from the true value by no more than 0.008. Use Normal approximation to determine the size of your Monte Carlo simulation.
- Based on the study in part (a), estimate the total weight, X, of the plastics produced in five days.
- Estimate Std(X) and comment on the accuracy of your estimator of X in part (a).
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