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Question 1 The BILLIS & CO warehouse runs a fleet of small cargo vehicles. Its Quality Assurance unit is concerned about hidden technical faults of these vehicles, which may cause work health and safety (WHS) issues. The company should decide whether to put the vehicles for inspection or not. The cost of finding a hidden technical fault (D, measured in AUD $) may vary between AUD $ 650 and AUD $ 810 depending on the service provider. There is also associated cost B (measured in AUD $) of sampling one vehicle for testing, which may vary between AUD $ 15 AUD and AUD $ 20.

The proportion of vehicles with hidden technical faults, Sj, is available from previous

studies and may be presented as the following probability distribution:

Proportion of faulty vehicles, Sj Probability P(Sj)

0.03 65%

0.05 15%

0.08 20%

If no vehicles are inspected, the cost of quality is calculated as x Sj x D, whereas the

cost of inspecting all vehicles in the fleet is x B.

a. Define and explain at least two decision alternatives that the company faces with

its quality assurance problem. Choose at random a single value for the parameters

D and B from the given range and use them for further calculations. Build the decision table and give explanation on the structure and calculations within.

b. Indicate and explain the recommended decision if the criterion for maximum

expected value is implemented.

c. Calculate the expected value of perfect information.

Question 2 Using historical data, a cargo insurance company, BestCarGO Ltd., estimated that the cost of damage caused by natural disasters in a given region is AUD $ 15,500 on average. BestCarGO Ltd. introduced several plans to prevent loss, and randomly sampled 200 policy holders. The survey showed a mean amount per claim to be AUD $ 14,930 with a standard deviation of AUD $ 4,031. Determine whether there is reason to believe the prevention plans were effective at the significance level of 0.05. Discuss the results.

this is the Task description & requirements The answer script must be typewritten; handwriting of the answers and formulas is not acceptable and subject to penalty at the discretion of the assessor. You need to present all the working of the calculations and, if using any statistical or calculation software e.g. Excel, provide the relevant result outputs with your answer. Refer to the textbook for worked examples on how to present answers. Result outputs can be produced as appendices but ensure the question number is clearly shown.