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Math Help - the normal dist

  1. #1
    Senior Member sfspitfire23's Avatar
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    the normal dist

    Hey guys,

    Cereal dispensing machine problem

    Suppose the standard deviation is not known but can be fixed at certain levels by adjusting the cereal dispensing machine. What is the largest std. dev. that will allow the actual value of cereal dispensed to fall within 1 ounce of the mean with prob of at least .95?

    The mean is 11.67 oz. per box of cereal.

    This involves Z-scores I'm pretty sure...
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    Are you looking for something like this?

    P(\mu- 2\sigma <Z < \mu+ 2\sigma) = 0.95

    P( 11.67- 2\sigma < Z< 11.67+ 2\sigma) = 0.95

    Solve for \sigma
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  3. #3
    Senior Member sfspitfire23's Avatar
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    Thanks for the response. I guess I'm confused as to how to solve this. Do I calculate the Z-score and set each equn. equal to that numer and solve for sigma?
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  4. #4
    Master Of Puppets
    pickslides's Avatar
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    Using symmetry

    P( 0 < Z< 11.67+ 2\sigma) = \frac{0.95}{2}

    P( Z< 11.67+ 2\sigma)- P(Z<0) = 0.475

    Now apply the inverse Z?
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