I read the following problem and I cannot get the right solution:
We consider a system of 12 sensors. The probability of one sensor to detect a signal with a magnitude higher than a is $p=\frac{1}{2\pi }\int_{x=a}^\infty \exp(\frac{-x^2}{2})$. What is the joint probability that 5 sensors detect this signal? It is stated that if $a=2.8$, the five signals yield to a joint probability corresponding to $5.7$
Thanks!