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Chapter 8 Review Exercises

Chapter 8 Review Exercises
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  • 13. Fire Insurance

    Assume that you are the owner of a home appliance company. You take out a $500,000 fire insurance policy on your factory. The annual premium is $2750. The probability of a fire is 0.005. What is the expected value?

    • Worked-Out Solution

      Notice that this is from the point of view of the policy holder.

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      _____    __   __   __   _    __   __   ______   
     / ____||  \ \\/ // | || | ||  \ \\/ // |      \\ 
    / //---`'   \ ` //  | '--' ||   \ ` //  |  --  // 
    \ \\___      | ||   | .--. ||    | ||   |  --  \\ 
     \_____||    |_||   |_|| |_||    |_||   |______// 
      `----`     `-`'   `-`  `-`     `-`'   `------`  
                                                      
    
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  • 14. Flood Insurance

    Assume that you are the owner of a home appliance company. You take out a $250,000 flood insurance policy on your factory. The annual premium is $3770. The probability of a flood is 0.014. What is the expected value?

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     __   _    __   __  __    __   __   __   _    _   
    | || | ||  \ \\/ // \ \\ / //  \ \\/ // | |  | || 
    | '--' ||   \ ` //   \ \/ //    \ ` //  | |/\| || 
    | .--. ||    | ||     \  //      | ||   |  /\  || 
    |_|| |_||    |_||      \//       |_||   |_// \_|| 
    `-`  `-`     `-`'       `        `-`'   `-`   `-` 
                                                      
    
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  • 15. Home Appliance Company

    Your company is considering developing one of two toaster models. Use a decision tree to decide which model your company should develop.

    • Worked-Out Solution

      Based on this decision tree, your company has a better expected value by developing toaster A.

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      _  __     ___     _____      _____    __   __  
     | |/ //   / _ \\  |  __ \\   |  ___||  \ \\/ // 
     | ' //   | / \ || | |  \ ||  | ||__     \   //  
     | . \\   | \_/ || | |__/ ||  | ||__     / . \\  
     |_|\_\\   \___//  |_____//   |_____||  /_//\_\\ 
     `-` --`   `---`    -----`    `-----`   `-`  --` 
                                                     
    
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  • 16. Home Appliance Company

    Assume that you are the owner of a home appliance company. Your company is considering developing one of two microwave models. Use a decision tree to decide which model your company should develop.

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      ____      _____     _____    __   __    _  _   
     |  _ \\   |  ___||  / ____||  \ \\/ //  | \| || 
     | |_| ||  | ||__   / //---`'   \ ` //   |  ' || 
     | .  //   | ||__   \ \\___      | ||    | .  || 
     |_|\_\\   |_____||  \_____||    |_||    |_|\_|| 
     `-` --`   `-----`    `----`     `-`'    `-` -`  
                                                     
    
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  • 17. Option Comparison

    Compare the two options.

    • Worked-Out Solution

      Based on this decision tree, option 2 has the greater expected value.

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      _  __   _    _      _____   __   __    _____   
     | |/ // | || | ||   / ___//  \ \\/ //  / ____|| 
     | ' //  | || | ||   \___ \\   \ ` //  / //---`' 
     | . \\  | \\_/ ||   /    //    | ||   \ \\___   
     |_|\_\\  \____//   /____//     |_||    \_____|| 
     `-` --`   `---`   `-----`      `-`'     `----`  
                                                     
    
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  • 18. Investment Comparison

    You want to invest $1000. Find the expected values for the two investments.

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     _____     _    _     _  _     _____    __   _   
    |  __ \\  | || | ||  | \| ||  |  ___|| | || | || 
    | |  \ || | || | ||  |  ' ||  | ||__   | '--' || 
    | |__/ || | \\_/ ||  | .  ||  | ||__   | .--. || 
    |_____//   \____//   |_|\_||  |_____|| |_|| |_|| 
     -----`     `---`    `-` -`   `-----`  `-`  `-`  
                                                     
    
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    system user
    Jackie (moderator)6 years ago |
    The worked-out solutions are only available for odd-numbered problems, so unfortunately we cannot show the work for this exercise.
    1
    system user
    Guest   6 years ago |
    Not sure of the solution
    0
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