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Normal distribution probability.

  • 05-12-2009 4:56pm
    #1
    Closed Accounts Posts: 138 ✭✭


    Having HUGE difficulties with this one if anybody has any suggestions as to where I need to start off. Would be much much appreciated.
    Thanks

    The predicted revenues from each site follow a Normal Distribution with the following parameters
    Site A: Mean = A1*, Std Dev = A2*
    Site B: Mean = B1*, Std Dev = B2*
    Site C: Mean = C1*, Std Dev = C2*

    What is the probability that
    the revenue on site B will be between $1,000,000 and $1,200,000
    the revenue on site C will be greater than $1,400,000
    the overall revenue on all three sites is over $4,000,000


Comments

  • Registered Users, Registered Users 2 Posts: 13,076 ✭✭✭✭bnt


    Do you have a book of statistical tables? This question basically requires you to look up values in a normal distribution "z-table", but first you have to standardize the values. This means by dividing their deviation from the mean by the standard deviation. For example, if the mean is $1,000, and the standard deviation is $200, then $700 and $1,300 are 1.5 standard deviations either side of the mean.

    You then take these values to the table, which gives you the probability that a test value is below the given value. (The tables have an helpful explanation, usually.) It's always given as below, so if you're looking for the probability it's above, you take 1 - z. To solve the "between" questions, you look up both values and subtract them. Drawing a quick graph of the distribution is helpful, and have a look at these worked examples to see if they make things clearer.

    You are the type of what the age is searching for, and what it is afraid it has found. I am so glad that you have never done anything, never carved a statue, or painted a picture, or produced anything outside of yourself! Life has been your art. You have set yourself to music. Your days are your sonnets.

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  • Closed Accounts Posts: 138 ✭✭Robbie444


    Thanks so much bnt :)


  • Closed Accounts Posts: 138 ✭✭Robbie444


    Oh just one thing, what does the * stand for?


  • Registered Users, Registered Users 2 Posts: 13,076 ✭✭✭✭bnt


    * usually means a footnote, a reference to something else in the document. Where you have A1, A2, etc. you need numbers, obviously, before you can work anything out, so I'm guessing the numbers are somewhere else in whatever document you have.

    You are the type of what the age is searching for, and what it is afraid it has found. I am so glad that you have never done anything, never carved a statue, or painted a picture, or produced anything outside of yourself! Life has been your art. You have set yourself to music. Your days are your sonnets.

    ―Oscar Wilde predicting Social Media, in The Picture of Dorian Gray



  • Closed Accounts Posts: 138 ✭✭Robbie444


    Just a bit confused about what value to put in for X in the equation for standardizing the values of A1, A2 etc

    The values are (*is irrelevant, sorry my mistake)
    A1= 1,000,000
    A2= 300,000
    B1= 1,100,000
    B2= 200,000
    C1= 900,000
    C2= 200,000

    so I have to use the formula Z= X-mean divided by standard deviation but how would I go about finding X here to do this standardization?
    Thanks


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  • Registered Users, Registered Users 2 Posts: 1,595 ✭✭✭MathsManiac


    X refers to any variable that's normally distributed with some specified mean and s.d., and Z is the standardised normally distributed variable given in the tables (whose mean is 0 and s.d. is 1).

    Your first question is asking "What is the probability that X lies between $1,000,000 and $1,200,000?" In order to use your z-tables to answer this, you need to convert it into "What is the probability that Z lies between ??? and ???" This is what you use your standardising formula for.

    So, in the first case, you use x=$1,000,000 to get a value for z, then use x=$1,200,000 to get another value for z, then try to use the tables to find the probability (i.e. the area) between these two z-values.

    If you can do that, you should manage the second part too.

    Get comfy with them before you look at the third part! For the third part, you need to use the fact that the sum of normally distributed variables is normally distributed: the mean of the resulting distribution is the sum of the individual means, and the variance (the s.d. squared) is the sum of the individual variances.


  • Closed Accounts Posts: 138 ✭✭Robbie444


    Hey thanks for the help, if X=1,000,000 though would the equation not look like 1,000,000-1,000,000(mean) / 300,000(standard deviation) since the mean here A1=1,000,000?


  • Closed Accounts Posts: 6,081 ✭✭✭LeixlipRed


    Yep, and what's 1,000,000 - 1,000,000?


  • Closed Accounts Posts: 138 ✭✭Robbie444


    got ya ;)


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