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kirill115 [55]
3 years ago
5

Please calculate the probability using the following equations (in document)

Mathematics
1 answer:
labwork [276]3 years ago
4 0

Substitute <em>u</em> = <em>t</em> ³/2592 and d<em>u</em> = <em>t</em> ²/864 d<em>t</em>. Then

P(T)=1-\displaystyle\int_0^T f(t)\,\mathrm dt=1-\displaystyle864\left(1.1574\times10^{-3}\right)\int_0^{\frac{T^3}{2592}}e^{-u}\,\mathrm du

The probability that a 12 hour surgery is successful is <em>P</em> (12), so letting <em>T</em> = 12 gives

P(12)\approx1-\displaystyle\int_0^{\frac23}e^{-u}\,\mathrm du\approx e^{-\frac23} \approx \boxed{0.5134}

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