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Math Help - help:( with standard deviation

  1. #1
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    Question help:( with standard deviation

    A manufacture of metal washer turn out washer with a mean of 4.5 g and a standard deviation of 0.047g, what is the probability that a randomly selected washer wall have a mass lees than 4.58g?
    Last edited by brandy; June 4th 2007 at 05:20 PM.
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  2. #2
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    Find the z-score:

    z=\frac{4.58 - 4.5}{.047} \approx 1.7

    Look up on Statistics tables the corresponding value which is .4554.

    So P(4.5\leq x \leq 4.58) = .4558

    Thus,
    P(x\leq 4.58) = P(x\leq 4.5)+P(4.5\leq x\leq 4.58) = .5+.4558 = .9558
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    Find the z-score:

    z=\frac{4.58 - 4.5}{.047} \approx 1.7

    Look up on Statistics tables the corresponding value which is .4554.

    So P(4.5\leq x \leq 4.58) = .4558

    Thus,
    P(x\leq 4.58) = P(x\leq 4.5)+P(4.5\leq x\leq 4.58) = .5+.4558 = .9558
    There is a slight problem here in that there is no standard for how tables
    of the standard normal distribution are presented.

    Now ImPerfectHackers table gives the probability that X takes a value
    between 0 and z (>0). However another common form of table
    gives the probability that X takes a value between -infty and the z, that
    is it is a table of the cumulative standard normal.

    If you use a software package to do this sort of thing the function used
    to give the probability will usually be like the second of the forms of table
    described rather than the former.

    RonL
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    Thumbs down I dont understand :(

    I am so confused can you explain to me?
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  5. #5
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    Quote Originally Posted by brandy View Post
    I am so confused can you explain to me?
    Ignore what CaptainBlank said. What do you not understand what I did?
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  6. #6
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    where...

    where did the .5 come from? I am not to sure? thanks!
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  7. #7
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    Quote Originally Posted by brandy View Post
    where did the .5 come from? I am not to sure? thanks!
    First I wrote P(x\leq 4.58) = P(x\leq 4.5)+P(4.5\leq x \leq 4.58)

    Now, P(4.5\leq x\leq 4.58) = .4558 because that was derived from the z-score.

    And P(x\leq 4.5)=.5 because it is the area of everything on the left hand side of the mean. Thus it is exactly 1/2.
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