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Math Help - mean of sample means?? ( confused.....)

  1. #1
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    mean of sample means?? ( confused.....)

    Quality control process show that the amount of the soft drink filled into can follow a normal distribution with mean of 330 ml and a standard deviation of 1.75 ml.

    a) Find the probability that a customer would purchase a can that contains more than 331.4 ml.
    The answer is 0.2119 (right??)

    b)If a customer randomly selects a pack of 12 cans as one sample, what is the probability that the AVERAGE AMOUNT of soft drink of the 12 cans will be more than 331.4 ml ???

    What is the answer in part B?? I feel confused.....
    Last edited by tiffany0658; March 25th 2014 at 08:09 AM.
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    Re: mean of sample means?? ( confused.....)

    Quote Originally Posted by tiffany0658 View Post
    Quality control process show that the amount of the soft drink filled into can follow a normal distribution with mean of 330 ml and a standard deviation of 1.75 ml.

    a) Find the probability that a customer would purchase a can that contains more than 331.4 ml.
    The answer is 0.2119 (right??)

    b)If a customer randomly selects a pack of 12 cans as one sample, what is the probability that the AVERAGE AMOUNT of soft drink of the 12 cans will be more that 331.4 ml ???

    What is the answer in part B?? I feel confused.....
    a) is correct.

    b) The average is just the sum of the amounts in the 12 cans divided by 12. You know how to add and scale normal random variables (right?) So do this to come up with the distribution for the average and then evaluate the probability just like you did in (a).
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    Re: mean of sample means?? ( confused.....)

    Can you show me the steps in question b ?
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    Re: mean of sample means?? ( confused.....)

    Quote Originally Posted by tiffany0658 View Post
    Can you show me the steps in question b ?
    If you take the average of N normal rvs each with mean $\mu$ and standard deviation $\sigma$ the resulting distribution is

    also normal with mean $\mu$ and standard deviation $\dfrac{\sigma}{\sqrt{N}}$

    so just do exactly what you did in (a) with the distribution $Normal\left(330, \dfrac{1.75}{\sqrt{12}}\right)$
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    Re: mean of sample means?? ( confused.....)

    the answer is 0.9972 ?
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    Re: mean of sample means?? ( confused.....)

    Quote Originally Posted by tiffany0658 View Post
    the answer is 0.9972 ?
    they ask for the probability the average will be greater than 331.4 ml, not less than it.
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  7. #7
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    Re: mean of sample means?? ( confused.....)

    0.0028?
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    Re: mean of sample means?? ( confused.....)

    ----
    Last edited by tiffany0658; March 25th 2014 at 09:49 AM.
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  9. #9
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    Re: mean of sample means?? ( confused.....)

    yes
    Thanks from tiffany0658
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