A stock with current value \(S(0)=100\) has an expected growth rate of its logarithm of \(u=12 \%\) and a volatility of that growth rate of \(\sigma=20 \%\). Find suitable parameters of a binomial lattice representing this stock with a basic elementary period of 3 months. Draw the lattice and enter the node values for 1 year. What are the probabilities of attaining the various final nodes?