1 Problem 13 9 A farming operation is located in a remote area that is more or less unreachable in the winter As early as September, the farmer must order fuel oil for the coming winter The amount of fuel oil he needs each winter is random, and depends on the severity of the winter weather to come The winter will be normal with probability 2 3 and very cold with probability 1 3 The numberofgallonsofoil the farmer needs to get through the winter is N(1,2 1) distributed in a normal winter and N(2,2 2) distributed in a very cold winter The farmer decides in September to stock up Q gallons of oil for the coming winter What is the probability that he will run out of oil in the coming winter What is the expected value of the number of gallons the farmer will come up short forthecomingwinter Whatistheexpectedvalueofthenumberofgallons he will have left over at the end of the winter

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Question: 1. Problem 13.9 A farming operation is located in a remote area that is more or less unreachable in the winter. As early as September,

1. Problem 13.9 A farming operation is located in a remote area that is more or less unreachable in the winter. As early as September, the farmer must order fuel oil for the coming winter. The amount of fuel oil he needs each winter is random, and depends on the severity of the winter weather to come. The winter will be normal with probability 2/3 and very cold with probability 1/3. The numberofgallonsofoil the farmer needs to get through the winter is N(μ1,σ2 1)

distributed in a normal winter and N(μ2,σ2 2) distributed in a very cold winter.

The farmer decides in September to stock up Q gallons of oil for the coming winter. What is the probability that he will run out of oil in the coming winter?

What is the expected value of the number of gallons the farmer will come up short forthecomingwinter?Whatistheexpectedvalueofthenumberofgallons he will have left over at the end of the winter?

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