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Math Help - Normal distribution

  1. #1
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    Normal distribution

    A container of 20ft carry a weight that is normally distributed with a mean of 5000 t and a standard deviation of 400 t. What percentage of container weight between 5400 and 5600 t?

    This is where I reached, how should I conclude on the percentage?
    For χ = 5400
    Z5400 = (5400-5000)/400
    Z5400 = 10
    For χ = 5600
    Z5600 = (5600-5000)/40
    Z5600 = 15
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  2. #2
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    Re: Normal distribution

    First you need to check your calculations.
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  3. #3
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    Re: Normal distribution

    Thank you. Corrected as;
    For χ = 5400
    Z5400 = (5400-5000)/400
    Z5400 = 1
    For χ = 5600
    Z5600 = (5600-5000)/400
    Z5600 = 1.5
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  4. #4
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    Re: Normal distribution

    Good.

    P(1<Z<1.5) = P(Z<1.5) - P(Z<1).

    Do you understand why and can you find these probabilities?
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  5. #5
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    Re: Normal distribution

    here is where I get confusion, distribution table I have I read for example from z column down to locate 1.5 and I get 0.4332 and for 1 0.3413. Help me how to read the values of 1.5 and 1
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  6. #6
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    Re: Normal distribution

    Quote Originally Posted by benedec View Post
    here is where I get confusion, distribution table I have I read for example from z column down to locate 1.5 and I get 0.4332 and for 1 0.3413. Help me how to read the values of 1.5 and 1
    Those will do but they are P(0<Z<1.5) and P(0<Z<1).

    The answer you need is still the difference between these two values.
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  7. #7
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    Re: Normal distribution

    was worried probably i read the table incorrectly, the difference i get is this; P(1<Z<1.5) = P(Z<1.5) P(Z<1) = 0.4332 0.3413 = 0.0919 = 9.19%
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