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Math Help - Mean, Mode, Median, Standard Deviation

  1. #1
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    Mean, Mode, Median, Standard Deviation

    Hi, any help on this would be appreciated!

    This question is as follows:

    1)Assume that the number of items borrowed per person per year in a library
    is normally distributed with a mean of 87 and a standard deviation of 4.
    These values describe the distribution of borrowing for the entire
    population of users in this library.

    a) What is the mode for this distribution?

    b) What is the median of this distribution?

    c) Roughly sketch the distribution. Place the number of items borrowed on
    the x axis and the number of individuals on the y axis. Indicate the
    location and values of the mean and the +two and +three standard deviations
    on the x axis.

    d)What percent of the population borrow between 83 and 91 items per year?

    e) What percent of the population borrow between 79 and 95 items per year?

    f) What percent of the population borrow more than 95 items per year?

    Work I've done:

    Not much. I'm having trouble knowing how to get started on the equation. I don't
    understand how having only the mean (87) and the standard deviation (4) is
    enough information to let me figure out the mode and median. It doesn't
    make sense to me.

    I know how to get the standard deviation from the mean when I have all of
    the data points, but there are no data points given in this problem
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  2. #2
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    Quote Originally Posted by logaw View Post
    Hi, any help on this would be appreciated!

    This question is as follows:

    1)Assume that the number of items borrowed per person per year in a library
    is normally distributed with a mean of 87 and a standard deviation of 4.
    These values describe the distribution of borrowing for the entire
    population of users in this library.

    a) What is the mode for this distribution?

    b) What is the median of this distribution?

    c) Roughly sketch the distribution. Place the number of items borrowed on
    the x axis and the number of individuals on the y axis. Indicate the
    location and values of the mean and the +two and +three standard deviations
    on the x axis.

    d)What percent of the population borrow between 83 and 91 items per year?

    e) What percent of the population borrow between 79 and 95 items per year?

    f) What percent of the population borrow more than 95 items per year?

    Work I've done:

    Not much. I'm having trouble knowing how to get started on the equation. I don't
    understand how having only the mean (87) and the standard deviation (4) is
    enough information to let me figure out the mode and median. It doesn't
    make sense to me.

    I know how to get the standard deviation from the mean when I have all of
    the data points, but there are no data points given in this problem
    You're also told that the random variable is normally distributed ......
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  3. #3
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    Ok, I have figured that part out. All three are the same.

    But I'm still not sure how to divide up the sections on the bell graph, or how to answer the rest of the questions.
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  4. #4
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    Quote Originally Posted by logaw View Post
    Ok, I have figured that part out. All three are the same.

    But I'm still not sure how to divide up the sections on the bell graph, or how to answer the rest of the questions.
    At this stage, I'd say you need to bring yourself up to speed with the normal distribution and its properties. I suggest you go back and carefully read some examples where probabilities are calculated using the normal distribution.
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  5. #5
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    Quote Originally Posted by mr fantastic View Post
    At this stage, I'd say you need to bring yourself up to speed with the normal distribution and its properties. I suggest you go back and carefully read some examples where probabilities are calculated using the normal distribution.

    Alright, thanks for the help!

    Edit: Nevermind, something clicked and I figured out what to do.

    Thanks again!
    Last edited by logaw; June 14th 2008 at 02:59 PM. Reason: solved
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