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    It is decided to increase the proportion of bottles which contain at least 750ml to 98%.
    (iv) This can be done by changing the value of μ, but retaining the original value of σ. Find the required value of μ.
    σ = 2.5

    Im stuck on how to do this question, i'm not really sure why you go about solving it as P(Z < (750 - μ)/2.5) = 0.02 instead of P(Z < (750 - μ)/2.5) = 0.98? Im also not really sure about why the < sign is used. any help would be appreciated.
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    (Original post by znx)
    It is decided to increase the proportion of bottles which contain at least 750ml to 98%.
    (iv) This can be done by changing the value of μ, but retaining the original value of σ. Find the required value of μ.
    σ = 2.5

    Im stuck on how to do this question, i'm not really sure why you go about solving it as P(Z < (750 - μ)/2.5) = 0.02 instead of P(Z < (750 - μ)/2.5) = 0.98? Im also not really sure about why the < sign is used. any help would be appreciated.
    What's the full question?
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    (Original post by znx)
    It is decided to increase the proportion of bottles which contain at least 750ml to 98%.
    (iv) This can be done by changing the value of μ, but retaining the original value of σ. Find the required value of μ.
    σ = 2.5

    Im stuck on how to do this question, i'm not really sure why you go about solving it as P(Z < (750 - μ)/2.5) = 0.02 instead of P(Z < (750 - μ)/2.5) = 0.98? Im also not really sure about why the < sign is used. any help would be appreciated.
    Please could you post the full question?

    From what I can tell, you are right in saying that P(Z<(750 - μ)/2.5) = 0.02, as 'at least' means you should use the > sign, so P(X>750)=0.98, therefore P(X<750)=1-P(X<750)=0.02, thus P(Z<(750 - μ)/2.5) = 0.02. It's hard to say though since I don't know the full question.

    Where did you get the P(Z < (750 - μ)/2.5) = 0.98 from? And what about using the < sign are you confused about?
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    Sorry the full question is:
    At a vineyard, the process used to fill bottles with wine is subject to variation. The contents of bottles are
    independently Normally distributed with mean μ = 751.4ml and standard deviation σ = 2.5ml.
    (i) Find the probability that a randomly selected bottle contains at least 750ml. [3]
    (ii) A case of wine consists of 6 bottles. Find the probability that all 6 bottles in a case contain at least 750ml. [2]
    (iii) Find the probability that, in a random sample of 25 cases, there are at least 2 cases in which all 6 bottles contain at least 750ml. [4]

    It is decided to increase the proportion of bottles which contain at least 750ml to 98%.
    (iv) This can be done by changing the value of μ, but retaining the original value of σ. Find the required value of μ
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    (Original post by gcsemusicsucks)
    Please could you post the full question?

    From what I can tell, you are right in saying that P(Z<(750 - μ)/2.5) = 0.02, as 'at least' means you should use the > sign, so P(X>750)=0.98, therefore P(X<750)=1-P(X<750)=0.02, thus P(Z<(750 - μ)/2.5) = 0.02. It's hard to say though since I don't know the full question.

    Where did you get the P(Z < (750 - μ)/2.5) = 0.98 from? And what about using the < sign are you confused about?
    I now know why they used the < sign but when I solve
    P(Z > (750 - μ)/2.5) = 0.98, I end up getting the incorrect value of μ.
    The answer is μ = 755.1
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    (Original post by znx)
    I now know why they used the < sign but when I solve
    P(Z > (750 - μ)/2.5) = 0.98, I end up getting the incorrect value of μ.
    The answer is μ = 755.1
    What value of z are you using?
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    (Original post by old_engineer)
    What value of z are you using?
    Φ^-1(0.98) which I get a z value of 2.054
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    (Original post by znx)
    Φ^-1(0.98) which I get a z value of 2.054
    OK there's your problem. You're looking at the wrong part of the bell curve. P(Z > z) = 0.98 is the same as P(Z =< z) = 0.02 and the value of z for which that is true is -2.054, not +2.054.
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    (Original post by old_engineer)
    OK there's your problem. You're looking at the wrong part of the bell curve. P(Z > z) = 0.98 is the same as P(Z =< z) = 0.02 and the value of z for which that is true is -2.054, not +2.054.
    Thank you that makes more sense now
 
 
 
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