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26 November, 19:17

From previous records a shipping company knows that the cost to deliver a small package within 24 hours is $15.50. The company charges $17.95 for shipping but guarantees to refund the full charge if the delivery is not made within 24 hours. If the company fails to deliver within the 24-hour window only 3% of the time, what is their expected gain per package?

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  1. 26 November, 19:35
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    Their expected gain per package is $1.9115

    Explanation:

    Expected gain per package

    = (what it gets if delivery is made) (probability delivery is made) + (what it loses if delivery is not made) (probability delivery is not made)

    = (17.95 - 15.50) * (0.97) + (-15.50) * (0.03)

    = 2.3765 - 0.465

    = 1.9115

    Therefore, Their expected gain per package is $1.9115
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