P(x)=e^-L*L^x/x! is the Poisson distribution formula where L represents lambda=2.2. P is the probability for x events, where x is 0, 1, 2, etc. If P=0.1967=e^-2.2*2.2^x/x!
e^-2.2=0.1108, so 2.2^x/x!=0.1967/0.1108=1.775 approx. Try x=3: 2.2^3/6=1.775 approx, so x=3.