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Math Help - Further Maths AS - S2 stuck on question!

  1. #1
    Newbie Femto's Avatar
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    Further Maths AS - S2 stuck on question!

    Ok maybe I'm not thinking clearly enough but here's the question with a stupid story to make it sound realistic:

    Q) The fluorescent light tubes made by the company "Well-lit" have lifetimes which are normally distributed with mean 2010 hours and standard deviation 20 hours. The company decides to promote its sales of the tubes by guaranteeing a minimum life of the tubes, replacing free of charge any tubes that fail to meet this minimum life.

    If the company wishes to have to replace free only 3% of the tubes sold, find the guaranteed minimum it must set.


    I've tried to make sense of the wording but I'm too slow to do that!

    So I know that \mu = 2010, \sigma = 20

    I think I need to do something with the 3% in order to get a number value which I can put into this equation:

    \frac{x - \mu}{\sigma}

    I'm just really confused with all the information; we've learnt how to do questions in stats but now they're in real life situations and it can get a tad confusing.

    I know I'm not as good as everyone here but I just need some help with this question
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  2. #2
    MHF Contributor
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    West Malaysia
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    Quote Originally Posted by Femto View Post
    Ok maybe I'm not thinking clearly enough but here's the question with a stupid story to make it sound realistic:

    Q) The fluorescent light tubes made by the company "Well-lit" have lifetimes which are normally distributed with mean 2010 hours and standard deviation 20 hours. The company decides to promote its sales of the tubes by guaranteeing a minimum life of the tubes, replacing free of charge any tubes that fail to meet this minimum life.

    If the company wishes to have to replace free only 3% of the tubes sold, find the guaranteed minimum it must set.


    I've tried to make sense of the wording but I'm too slow to do that!

    So I know that \mu = 2010, \sigma = 20

    I think I need to do something with the 3% in order to get a number value which I can put into this equation:

    \frac{x - \mu}{\sigma}

    I'm just really confused with all the information; we've learnt how to do questions in stats but now they're in real life situations and it can get a tad confusing.

    I know I'm not as good as everyone here but I just need some help with this question
    If only 3% of the bulbs do not meet the requirement, then solve

    P(X<=k)=0.03 where k is the minimum lifetime.
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  3. #3
    Newbie Femto's Avatar
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    Quote Originally Posted by mathaddict View Post
    If only 3% of the bulbs do not meet the requirement, then solve

    P(X<=k)=0.03 where k is the minimum lifetime.
    Oh thank you so much; so all I need to do is find the number for 97% and make it negative? Then stick the numbers into that equation \frac{x - \mu}{\sigma}? Or not?
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