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Math Help - mean and sd

  1. #1
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    mean and sd

    Hiya...

    I'm unsure where to start with this question...

    The weights of cans of pears produced by a local canning factory are normally distributed with a mean of 500 grams and a standard deviation of 25 grams. Calculate the percentage of cans that weigh:

    a. 430 grams or less.
    b. between 525 and 550 grams.

    Thanks!
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  2. #2
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    Quote Originally Posted by bennyya View Post


    b. between 525 and 550 grams.
    The probability between 500 and 550 is 47.5% (2 standard deviations)
    The probability between 500 and 525 is 34% (1 standard deviation)
    Thus,
    Probability between 525 and 550 is 47.5%-34%=13.5%
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  3. #3
    Senior Member
    Joined
    Jul 2006
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    correct me if i'm wrong but i think you can do this with the Texas Instruments Ti-83 calc.
    for question A)
    if you go 2nd->DISTR (above VARS) -> 2: normalCdf (-1*10^99, 430, 500, 25)
    it will give you roughly 0.0026 which is 0.256% of cans will be 430 grams or less.
    Its a very small number, but dont forget its almost 3 std. dev's off the mean.
    if it were 3 std. dev's off the mean it would have a probability of (1 - 0.997)/2 = 0.0015 = 0.15%.

    Hope this helps
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