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Math Help - Given Mean and SD, find Prob Distribution

  1. #1
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    Given Mean and SD, find Prob Distribution

    I'm a little confused by this problem which seems simple, but I'm not really sure how to solve it.

    >
    It says: The number of hamburgers ordered in a day is normally distributed with a Mean of 45 and Standard Deviation of 8.4, Then asks:

    What is the probability Distribution (type of distribution, mean and Standard Deviation) of the average hamburgers ordered for 50, 100, 1000 Customers?
    <

    Would the type of distribution just be normal for all 3 sizes, or is there a way to calculate the type distribution?

    I'm not sure how to calculate the mean and SD for a already given mean and SD, when you are just given what I guess is the sample size. I have a formula to calculate the Standard deviation of the Sample Mean which is:

    Standard Deviation / Square root of the sample size

    But I'm not sure if these numbers, 50, 100, 1000 are sample mean sizes.

    Thanks for any help.
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  2. #2
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    Quote Originally Posted by Cadag View Post
    I'm a little confused by this problem which seems simple, but I'm not really sure how to solve it.

    >
    It says: The number of hamburgers ordered in a day is normally distributed with a Mean of 45 and Standard Deviation of 8.4, Then asks:

    What is the probability Distribution (type of distribution, mean and Standard Deviation) of the average hamburgers ordered for 50, 100, 1000 Customers?
    <

    Would the type of distribution just be normal for all 3 sizes, or is there a way to calculate the type distribution?

    I'm not sure how to calculate the mean and SD for a already given mean and SD, when you are just given what I guess is the sample size. I have a formula to calculate the Standard deviation of the Sample Mean which is:

    Standard Deviation / Square root of the sample size

    But I'm not sure if these numbers, 50, 100, 1000 are sample mean sizes.

    Thanks for any help.
    Sorry but this makes no sense to me.
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  3. #3
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    So Cadag, did you ever figure this problem out?
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  4. #4
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    Quote Originally Posted by Cadag View Post
    It says: The number of hamburgers ordered in a day is normally distributed with a Mean of 45 and Standard Deviation of 8.4, Then asks:

    What is the probability Distribution (type of distribution, mean and Standard Deviation) of the average hamburgers ordered for 50, 100, 1000 Customers?
    Very strange question, it does say the data is normally distributed so it would remain normal for all sample sizes >30 otherwise consdier the student's t-distribution.

    Maybe the question is just wanting you to declare the sample mean and standard deviation for each sample size ie.

     n = 50 : X \sim N(\mu,(\frac{\sigma}{\sqrt{50}})^2 )

     n = 100 : X \sim N(\mu,(\frac{\sigma}{\sqrt{100}})^2 )


    Quote Originally Posted by Cadag View Post
    I'm a little confused by this problem which seems simple, but I'm not really sure how to solve it.

    >

    I'm not sure how to calculate the mean and SD for a already given mean and SD, when you are just given what I guess is the sample size. I have a formula to calculate the Standard deviation of the Sample Mean which is:

    Standard Deviation / Square root of the sample size

    But I'm not sure if these numbers, 50, 100, 1000 are sample mean sizes.
    Your formula to calculate the smaple mean is correct.

     n = 50 : \bar{x} = \frac{\sigma}{\sqrt{n}} =\frac{8.4}{\sqrt{50}}

     n = 100 : \bar{x} = \frac{\sigma}{\sqrt{n}} =\frac{8.4}{\sqrt{100}}

    and so on
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  5. #5
    MHF Contributor matheagle's Avatar
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    CORRECTION...

     n = 50 : \sigma_{\bar{x}}= \frac{\sigma}{\sqrt{n}} =\frac{8.4}{\sqrt{50}}

     n = 100 : \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} =\frac{8.4}{\sqrt{100}}
    Last edited by matheagle; April 28th 2009 at 11:19 PM.
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