Prob. for Difference of mean, single finite pop.

rogo0034
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Homework Statement



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Homework Equations



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The Attempt at a Solution

 
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not entirely sure what to do here, i mean I've gotten the Variance for each, 78.125 & 50, and then... I'm confused because it's coming from one population, not two. hmmf.
 
A: .0119 and .0024 respectively, for the prob of being over 20, is this at all right?

B:So I put them each into the central limit theorem and got: .1892 for the first and .1591 for the second
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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