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Math Help - P( |b1 - b2 |> 0.1) = 2p( b1 - b2 > 0.1)

  1. #1
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    Cool P( |b1 - b2 |> 0.1) = 2p( b1 - b2 > 0.1)

    Can any one tell me
    How we can write P( |B1 - B2 |> 0.1)
    equals to 2P( B1 - B2 > 0.1)
    Please explain.
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  2. #2
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    Quote Originally Posted by Sashikala View Post
    Can any one tell me
    How we can write P( |B1 - B2 |> 0.1)
    equals to 2P( B1 - B2 > 0.1)
    Please explain.
    This is clearly not a chat topic. It's a statistics question and would better belong in one of the two statistics subforums.

    What is B1? A random variable? What distribution does it follow? What is B2? The whole question is needed, not just the small scraps you've decided are important.
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  3. #3
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    Cool Statistics

    B1,B2 are random variables and they follow normal distribution.
    The full question is:
    Bottles of mineral water are delivered to shops in crates containing 12 bottles each. The weights of bottles are normally distributed with mean weight 2kg and standard deviation 0.05kg. The weights of empty crates are normally distributed with mean 2.5kg and standard deviation 0.3kg.
    Two bottes are selected at random from a crate. Find the probability that they differ in weight by more than 0.1kg.
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  4. #4
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    Quote Originally Posted by Sashikala View Post
    B1,B2 are random variables and they follow normal distribution.
    The full question is:
    Bottles of mineral water are delivered to shops in crates containing 12 bottles each. The weights of bottles are normally distributed with mean weight 2kg and standard deviation 0.05kg. The weights of empty crates are normally distributed with mean 2.5kg and standard deviation 0.3kg.
    Two bottes are selected at random from a crate. Find the probability that they differ in weight by more than 0.1kg.
    Let B1 and B2 be the random variables weight of first bottle and second bottle. You know they are both normally distributed with mean and standard deviation as given.

    Then B = B1 - B2 is also a normally distributed random variable. Its mean is zero and standard deviation is 0.05 \sqrt{2}. Read section 3 of this: Normal distribution - Wikipedia, the free encyclopedia

    Calculate Pr(-0.1 < B < 0.1) = 2 Pr(0 < B < 0.1) by symmetry.
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  5. #5
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    Wink Statistics

    Mr Fantastic
    Thanks very much.
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  6. #6
    MHF Contributor matheagle's Avatar
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    We always have P( |B1 - B2 |> 0.1)=P( B1 - B2> 0.1)+P( B1 - B2 <- 0.1).
    NOW, if this random variable B1 - B2 is symmetric then those two probabilities are equal and you do get
    =2P( B1 - B2> 0.1).
    Last edited by matheagle; March 24th 2009 at 06:59 AM.
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  7. #7
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    Smile Statistics

    MathEagle,
    Thanks very much.
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