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Math Help - Standard deviations

  1. #1
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    Standard deviations

    Nylon strands are manufactured to a mean tensile strength of 1.5 N, with a standard deviation of 0.04N. If the tensile strength of strands is normally distributed
    a) what percentage of the strands would have a strength of less than 1.4 N, and will be recycled?
    b) what range of strengths, symmetrical about the mean, would you expect 90% of the strands to be recycled?

    a) I got the answer to this one. Just by using the z score formula and looking it up on the table and such its 0.62%

    b) this is the question that I am having issues with
    here is what i did:
    area to left (looked up on table) = .9015 which is a z score of 1.29
    plugged into formula
    1.29 = (x-1.5)/.04
    multiply both sides by .04
    0.0516 = x-1.5
    x = 1.5516

    I know you are supposed to do something like that but i do not know how to get this "range" they are talking about.. this is probably due to the fact i have no idea what symmetrical about the mean means... i can't find the information about this anywhere..

    the answer in the back of the book is 1.43N to 1.57N
    -in a sense i'm sort of close...
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  2. #2
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    The range will be \pm a such that P\left( Z<\frac{a-1.5}{0.04}\right) = 0.05
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  3. #3
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    i'm not sure i understand...
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  4. #4
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    90% symmetrical around the mean. Imagine the 100% is broken into intervals 5%-90%-5% = 0.05-0.9-0.05

    Is this any better?
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