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Math Help - Simple question

  1. #1
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    Simple question

    Burger hack claims that the mean number of grams of fat in its Lotta Burger is 24 grams with a standard deviation of 5 grams. If a sample of 50 Lotta Burgers is taken, what is the probability that the sample mean is 25 grams or more?

    I think I found the answer but really dont understand why.

    ty
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  2. #2
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    Quote Originally Posted by Nhimrod View Post
    Burger hack claims that the mean number of grams of fat in its Lotta Burger is 24 grams with a standard deviation of 5 grams. If a sample of 50 Lotta Burgers is taken, what is the probability that the sample mean is 25 grams or more?

    I think I found the answer but really dont understand why.

    ty
    The sample size n = 50 is large. The population size N can be assumed infinite.

    Then the distribution of \bar{x} is normal with mean \mu = 24 and standard deviation \frac{\sigma}{\sqrt{n}} = \frac{5}{\sqrt{50}} = \frac{1}{\sqrt{2}}.

    Calculate \Pr(\bar{x} > 25).

    I get 0.0786 (correct to four decimal places).
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