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I'm having trouble trying to solve this question, the context is pH acidity in rain: mean = 3.719 sd = 0.546

You are given that the probability that a rainfall collection has a pH less than 3.2 is 0.17. In a random sample of 10 rainfall collections, find the probability that exactly one has a pH less than 3.2

I'm not sure if this is asking for sample calculations, or independent events or what?

Cheers

Edit: this is a normal distribution

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Given that $Prob(pH < 3.2) = 0.17$ and assuming that all 10 rainfall collections are independent, your random variable (the number of rainfall collections with a pH below $3.2$) is binomially distributed. So,

$Pr(X=1) = {10 \choose 1} p (1-p)^9 = 1·0.17·(0.83)^9 = 0.3178$

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  • $\begingroup$ typo: $\left({10\atop 1}\right)=10$. The endresult is okay. $\endgroup$
    – drhab
    Commented Oct 24, 2013 at 18:02

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