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Math Help - Don't Understand the Question

  1. #1
    Member WhoCares357's Avatar
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    Don't Understand the Question

    I have this problem for homework:

    Light bulbs are measured in lumens (light output), watts (energy used), and hours (life). A standard white light bulb has a mean life of 675 hours and a standard deviation of 50 hours. A soft white light bulb has a mean life of 700 hours and a standard deviation of 35 hours. At a local science competition, both light bulbs lasted 750 hours. Which light bulb’s life span was better? Explain.
    I'm not sure what it's asking. Does it want me to find the largest area covered by the bulb's life and base the best life span on that or does it want me to base it on how much area is left?

    PS This worksheet is on the bell-shaped curve, the mean and standard deviation.
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  2. #2
    Junior Member mathhomework's Avatar
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    Trying to Help

    I am just trying to help. I am not sure of the answer. Experts please check my answer. Thank you.

    I think the Soft White Bulb has a longer life span,

    because its mean, which is an average, is 700, this means that most Sofe White Bulb can last 700 hours, and its standard deviation is 35, which is a smaller spread compare to 50, the Standard White Bulb; therefore, compare to the one time 750 record, the Soft White Bulb is better.
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  3. #3
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    Quote Originally Posted by WhoCares357 View Post
    I have this problem for homework:



    I'm not sure what it's asking. Does it want me to find the largest area covered by the bulb's life and base the best life span on that or does it want me to base it on how much area is left?

    PS This worksheet is on the bell-shaped curve, the mean and standard deviation.
    The problem statement is far from clear, but I think they are asking you to find \Pr(\text{life} \geq 750) for the two types of bulbs. Presumably the less likely event is "better". I guess.
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  4. #4
    Member WhoCares357's Avatar
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    I actually posted this on another website: What Constitutes "better"? - Statistics Help @ Talk Stats Forum

    Someone there told me to use the z-score. He has not told me why yet, but now I'm not too sure if I should use that :/.
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  5. #5
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    Quote Originally Posted by WhoCares357 View Post
    I actually posted this on another website: What Constitutes "better"? - Statistics Help @ Talk Stats Forum

    Someone there told me to use the z-score. He has not told me why yet, but now I'm not too sure if I should use that :/.
    It should be clear from post #3 why you might want to calculate z-scores. The globe with the higher z-score will be the 'better' bulb (do you see why? - go back and read post #3).
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  6. #6
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    Quote Originally Posted by mr fantastic View Post
    It should be clear from post #3 why you might want to calculate z-scores. The globe with the higher z-score will be the 'better' bulb (do you see why? - go back and read post #3).
    I think I get it. Thanks for all the help .
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