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Math Help - normal distribution, find standard deviation

  1. #1
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    Exclamation normal distribution, find standard deviation

    please help me! i am a little bit stuck!

    a farmer supplies tomatoes to a grocery, with an average weight of 74 grams
    weight of tomatoes is normally distributed about their mean
    grocery has policy of rejecting tomatoes that weigh less than 70 grams
    11% of the farmer's tomatoes have been rejected
    what is the standard deviation?

    i know z=(x-mean)/stdev, x=70, mean=74, P(X<70)=0.11 but i'm totally mind-blanking on how to find z and also stdev.
    i think P(x<70)=P(Z<z), is that right?
    any help is very much appreciated!
    many thanks!!
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  2. #2
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    Quote Originally Posted by lalalamaths View Post
    please help me! i am a little bit stuck!

    a farmer supplies tomatoes to a grocery, with an average weight of 74 grams
    weight of tomatoes is normally distributed about their mean
    grocery has policy of rejecting tomatoes that weigh less than 70 grams
    11% of the farmer's tomatoes have been rejected
    what is the standard deviation?

    i know z=(x-mean)/stdev, x=70, mean=74, P(X<70)=0.11 but i'm totally mind-blanking on how to find z and also stdev.
    i think P(x<70)=P(Z<z), is that right?
    any help is very much appreciated!
    many thanks!!
    Find the value of z^* such that \Pr(Z < z^*) = 0.11.

    From Z = \frac{X - \mu}{\sigma} you therefore have z^* = \frac{70 - 74}{\sigma}. Substitute the value of z^* and then solve for \sigma.
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  3. #3
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    thanks for your reply! how do i find z* though? i'm probability-zonked
    is it using normdist? or z-tables?
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  4. #4
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    Quote Originally Posted by lalalamaths View Post
    thanks for your reply! how do i find z* though? i'm probability-zonked
    is it using normdist? or z-tables?
    Use tables.

    Note: Pr(Z < z*) = 0.11 => Pr(Z > -Z*) = 0.11 => Pr(Z < -z*) = 0.89. Using my old Kaye and Laby Four Figure Mathematical Tables I get -z* = 1.227 => z* = -1.277.
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