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Some stats help - positively skewed distributions.

  • 27-11-2007 3:28am
    #1
    oq4v3ht0u76kf2
    Closed Accounts Posts: 2,028 ✭✭✭


    Hi folks,

    Doing some revision for exams after Christmas and came across this problem written at the bottom of one of my tutorial sheets:
    Mean rent for an apartment in the USA is $1200 / month and the distribution is positively skewed.

    What is the probability of selecting a sample of 50 apartments and the mean being $950? The standard deviation of the sample is $250.

    I have literally no idea how to start attacking this question. The book I'm using for revision (Business Mathematics and Statistics, 6th Ed., Francis) is not helping but I am worried I am missing something elementary from the question that I may have forgotten to write down.

    As far as I can tell, my first step is to estimate the mode or the 1st / 3rd inter-quartile values but it seems very vague that way. Can anybody point me in the right direction?

    Cheers,
    Rob


Comments

  • #2
    2Scoops
    Registered Users, Registered Users 2 Posts: 1,845 ✭✭✭2Scoops


    With a sample size of 50, the hypothetical sample mean should have a normal distribution, even if the population distribution is positively skewed (central limit theorem). The standard deviation of a sample mean is the standard error, hence 250/root50 , or ~35.

    Then get a Z-score for where 950 would fall on this distribution.
    z-score = (score - mean)/standard deviation
    = (950-1200)/35
    = ~ -7
    Consult some log tables to get the probability but with a Z-score like that, I’m guessing very, very improbable! :)


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