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Weight varies approximately to the normal distribution in a population of adolescents. The population mean is 17.8 and the standard deviation is 1.9. What is the probability of randomly selecting a child whose weight is greater than 21.6 based on a sample of 15 children?

So that's the question given, and I'm wondering how to approach this question using sampling distributions. The question would be that typical sampling distribution of means question if it was asking for the average BMI, but it's not. How would I solve this question?

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If you selected just one child at random, the probability he would be obese is the probability $ p = \mathbb P(X \geq 2 ) $ with $ X \sim N(0, 1) $, which is $ \approx 0.0227 $. (Note that $ 21.6 = 17.8 + 2 \cdot 1.9 $.) If you pick $ 15 $ children at random, the probability at least one of them are obese is $ 1 - (1-p)^{15} $, which by explicit computation is equal to $ 0.291\ldots $

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  • $\begingroup$ Oh so the question isn't solved by using sampling distributions but through elementary probability theories! Thanks for the answer. $\endgroup$
    – minnn
    May 10, 2020 at 14:52

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