A trucking company delivering bags of cement to suppliers has a fleet of trucks whose mean unloaded weight is 6700 kg with a standard deviation of 100 kg. They are each loaded with 800 bags of cement...

Extracted text: A trucking company delivering bags of cement to suppliers has a fleet of trucks whose mean unloaded weight is 6700 kg with a standard deviation of 100 kg. They are each loaded with 800 bags of cement which have a mean weight of 44 kg and a standard deviation of 3 kg. The trucks travel in a convoy of four and pass over a weigh scale en route. a) The government limit on loaded truck weight is 42,000 kg. Exceeding this limit by (i) less than 125 kg results in a fine of $200, (ii) between 125 and 200 kg results in a fine of $400 and (iii) over 200 kg yields a fine of $600. What is the expected fine per truck? b) In addition to the above, the government charges a special road tax if the mean loaded weight of the trucks in a convoy of four trucks is greater than 42,000 kg. What is the probability that any particular convoy will be charged this tax?