Ebola: 85% Mortality Rate & Mean of 100000 Contractors

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the deadly Ebola virus kills 85% of those who contract it. Of the next 100000 people who contract it, what is the mean number who will die?
 
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And your thoughts on the matter are___________?
 
I'm thinking it's:

85% of 100 000 which is 85 000 but I'm not really sure of that
 
Why not?
 
The mean is the "expected value". You are told that 85% die. Of 1000000 people, how many would you expect to die?
 
if it's 85% of 100 000 then 85 000 will die
 
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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