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  1. #1 S.D. 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    Can anyone help me with this question??

    The mean height of players in a a basketball competition is 184cm. If the standard deviation is 5cm, what percentage of them are likely to be:

    i) taller than 189cm
    ii)taller than 179cm
    iii)between 174cm and 199cm
    iv) over 199cm tall?

    thank you


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  3. #2  
    Forum Professor jrmonroe's Avatar
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    How far have you gone in your calculations or understanding of the problem?


    Grief is the price we pay for love. (CM Parkes) Our postillion has been struck by lightning. (Unknown) War is always the choice of the chosen who will not have to fight. (Bono) The years tell much what the days never knew. (RW Emerson) Reality is not always probable, or likely. (JL Borges)
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  4. #3  
    Moderator Moderator AlexP's Avatar
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    Given a normal distribution, there are certain percentages that correspond to certain standard deviations. I'm sure you can find these percentages online, and once you have them, the answers to your questions should be very easy to obtain.
    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
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  5. #4 Re: S.D. 
    . DrRocket's Avatar
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    Quote Originally Posted by Heinsbergrelatz
    Can anyone help me with this question??

    The mean height of players in a a basketball competition is 184cm. If the standard deviation is 5cm, what percentage of them are likely to be:

    i) taller than 189cm
    ii)taller than 179cm
    iii)between 174cm and 199cm
    iv) over 199cm tall?

    thank you
    As Alexp said, if the distribution is normal your questions can be answered using a table for the normal distribution.. It is not possible to calculate the answers exactly but the necessary integral has been approximated numerically and the results tabulated -- which is what the table for the normal distribution really is.

    On the other hand this question, with no further qualification, demonstrates a fundamental lack of understanding of probability theory on the part of whoever formulated the question. Unless you know the form of the distribution there is no a priori relationship between the standard deviation and probabilities. Moreover, I can guarantee that the height of basketball players is not exactly normally distributed -- if it were there would eventually be a basketball player of negative height.
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  6. #5  
    Forum Masters Degree organic god's Avatar
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    height is typically normally distributed, maybe its not exactly normally distributed but it is a good approximation.
    everything is mathematical.
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  7. #6  
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    Quote Originally Posted by organic god
    height is typically normally distributed, maybe its not exactly normally distributed but it is a good approximation.
    How good the approximation is depends entirely on your purpose.

    I can guarantee that the height is not precisely normally distributed.
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  8. #7  
    Forum Masters Degree organic god's Avatar
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    yes, you can guarantee this,

    However if a probability distribution is needed, the exact form of it is often not known, however it will not be too dissimilar from a normal distribution.

    Therefore for a theoretical basketball population, a normal distribution is the best one available
    everything is mathematical.
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  9. #8  
    . DrRocket's Avatar
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    Quote Originally Posted by organic god
    yes, you can guarantee this,

    However if a probability distribution is needed, the exact form of it is often not known, however it will not be too dissimilar from a normal distribution.

    Therefore for a theoretical basketball population, a normal distribution is the best one available
    One more time. That depends entirely on your application.

    There is zero justification for your statement.

    The usual justification for use of the normal distribution is the application of the central limit theorem. That does not apply in this case.

    The real reason that the normal distribution is used so commonly is that it is easy to do calculations if things are normally distributed.
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  10. #9 Re: S.D. 
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    Quote Originally Posted by Heinsbergrelatz
    Can anyone help me with this question??

    The mean height of players in a a basketball competition is 184cm. If the standard deviation is 5cm, what percentage of them are likely to be:

    i) taller than 189cm
    ii)taller than 179cm
    iii)between 174cm and 199cm
    iv) over 199cm tall?

    thank you

    Just answer "Ir is impossible to say" for all three.

    You might not get any marks for ir but you will be right!!
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  11. #10  
    Forum Masters Degree organic god's Avatar
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by organic god
    yes, you can guarantee this,

    However if a probability distribution is needed, the exact form of it is often not known, however it will not be too dissimilar from a normal distribution.

    Therefore for a theoretical basketball population, a normal distribution is the best one available
    One more time. That depends entirely on your application.

    There is zero justification for your statement.

    The usual justification for use of the normal distribution is the application of the central limit theorem. That does not apply in this case.

    The real reason that the normal distribution is used so commonly is that it is easy to do calculations if things are normally distributed.
    One more time

    In this situation, the probability distribution is not known, the question is used to test the students understanding of the normal distribution.

    I don't see why this is upsetting you so much
    everything is mathematical.
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  12. #11  
    . DrRocket's Avatar
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    Quote Originally Posted by organic god
    Quote Originally Posted by DrRocket
    Quote Originally Posted by organic god
    yes, you can guarantee this,

    However if a probability distribution is needed, the exact form of it is often not known, however it will not be too dissimilar from a normal distribution.

    Therefore for a theoretical basketball population, a normal distribution is the best one available
    One more time. That depends entirely on your application.

    There is zero justification for your statement.

    The usual justification for use of the normal distribution is the application of the central limit theorem. That does not apply in this case.

    The real reason that the normal distribution is used so commonly is that it is easy to do calculations if things are normally distributed.
    One more time

    In this situation, the probability distribution is not known, the question is used to test the students understanding of the normal distribution.

    I don't see why this is upsetting you so much
    I am not upset at all. Read my posts more carefully.

    I have simply pointed out the unstated and not necessarily true assumptions that have been made by whoever wrote the question.

    I understand what the questioner intended the sudent to do. I also understand why that is an exercise in blindly applying a formula that may or may not be appropriate, depending on what one is really trying to do.

    Probability theory is deeper than many statisticians appreciate.

    Recognizing that the probability distribution is not known is the starting point for recognizing the potential errors in applying formulas by rote.
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