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Math Help - Normal Distribution Question

  1. #1
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    Normal Distribution Question

    Hi, i have this question

    The weight of a box of cereal has a normal distribution with mean = 340g and standard deviation = 5g.

    (c) 30 boxes of this cereal are selected at random for weighing. Find the probability that the sample variance is more than 36.69.
    how do i solve this? thank you.

    Regards,

    tommy
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  2. #2
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    Quote Originally Posted by tommyhakinen View Post
    Hi, i have this question

    The weight of a box of cereal has a normal distribution with mean = 340g and standard deviation = 5g.

    (c) 30 boxes of this cereal are selected at random for weighing. Find the probability that the sample variance is more than 36.69.

    how do i solve this? thank you.

    Regards,

    tommy
    You should know that when samples of size n are taken from a normal population with variance \sigma^2 then

    \frac{n-1}{\sigma^2} S^2 ~ \chi^2_{n-1}

    where S^2 is the random variable variance of sample.

    So for your problem \frac{29}{25} S^2 ~ \chi^2_{29}.

    \Pr\left( S^2 > 36.69\right) = \Pr\left( \frac{29}{25} \, S^2 > \left( \frac{29}{25} \right) \, 36.69 = 42.5604\right) = \Pr(\chi^2_{29} > 42.5604) = 0.05, correct to two decimal places.
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