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Math Help - Calculating a Normal Distribution With a Set Mean

  1. #1
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    Calculating a Normal Distribution With a Set Mean

    Hello,

    I came across a problem that I was hoping to get some help on.

    I have ~$3,260 to spend on 6 different items priced at:

    $5 each
    $5.50 each
    $7.70 each
    $10 each
    $11 each
    $15 each

    I also need the mean across all items to be equal to ~$8.36.

    It doesn't really matter if I'm slightly above, or slightly below the average amount/total amount, but the count of each item has to be a whole number (I can't buy 1/2 a $5 item).

    Does anyone know of a formula out there that would allow me to calculate how many of each I require if I assume a normal distribution?

    Moreover, something that would be reusable for if I were to have ~$469 to buy the same 6 items where the mean across all items are equal to ~$7.10?

    Thank you in advance!
    Rob
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  2. #2
    MHF Contributor
    Joined
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    Australia
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    Re: Calculating a Normal Distribution With a Set Mean

    Hey Rob636.

    You still need to decide what the variance is (to have a specific normal distribution).

    Once you do that, then you can calculate the probabilities of "bins" (example: one bin might be $4 - $5) and then use that to describe what the probability of getting certain prices.

    To obtain probabilities, you should use a calculator or computer program which should be available after a quick google search. You can also use R which is a free package and use the pnorm command to get probabilities.
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