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Thread: Finding an approximation? (Continuity Correction?)

  1. #1
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    Finding an approximation? (Continuity Correction?)

    Hello everyone hope you're all having a good day, this question has been bugging me on a past paper I have been practicing for two days.

    The question is:
    The Colosseum in Rome can be divided into several thousand small sections.Suppose that the earthquake force that a section can withstand has meanand standard deviation, respectively, of 3.4 and 1.5 on the Richter scale. Arandom sample of 100 sections is taken. Find an approximation to theprobability that the mean earthquake force that these can withstand isgreater than 3.6 on the Richter scale.

    My first assumption was to use the continuitycorrection if we approximate it by a continuous distribution like the normal. But i'm having trouble applying this concept and identifying what key points I need to extract from the question.
    Any help would be appreciated.

    Thank you
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  2. #2
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    Re: Finding an approximation? (Continuity Correction?)

    you've got a population that's distributed as that's $normal(3.4,1.5)$

    You then sample this population, taking 100 samples, and find the mean of the force these samples can withstand.

    You should know that the distribution of the mean, $\bar{X}$ of a set of samples of a $normal(\mu,\sigma)$ population is

    $\bar{X} \sim normal\left(\mu, \dfrac{\sigma}{\sqrt{n}}\right)$

    $P[\bar{X} > 3.8] = 1 - P[\bar{X} \leq 3.8] = 1 - \Phi\left(\dfrac{3.8-3.4}{\dfrac{1.5}{\sqrt{100}}}\right) = 1 - \Phi\left(2\dfrac 2 3\right) \approx 0.996$
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  3. #3
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    Re: Finding an approximation? (Continuity Correction?)

    Quote Originally Posted by elijah123 View Post
    Hello everyone hope you're all having a good day, this question has been bugging me on a past paper I have been practicing for two days.

    The question is:
    The Colosseum in Rome can be divided into several thousand small sections.Suppose that the earthquake force that a section can withstand has meanand standard deviation, respectively, of 3.4 and 1.5 on the Richter scale. Arandom sample of 100 sections is taken. Find an approximation to theprobability that the mean earthquake force that these can withstand isgreater than 3.6 on the Richter scale.

    My first assumption was to use the continuitycorrection if we approximate it by a continuous distribution like the normal. But i'm having trouble applying this concept and identifying what key points I need to extract from the question.
    Any help would be appreciated.

    Thank you
    Since the values of mean and sd are both given to one decimal place and the Richter scale is a continuous scale, then it assumed that these values have been rounded.
    "Greater than 3.6" can therefore be interpreted as greater than (or equal to, which is the same for continuous distributions) 3.55 as 3.54999... would be rounded to 3.5 not 3.6.
    Thanks from elijah123
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