Finance Exam involving: Options, Stochastic Processes, Binomial Model, Black-Scholes Model

Example:

A variable is currently 40

It follows a Markov process

Processis stationary (i.e. the parameters of the process do not change as we move through time)

At the end of 1 year the variable will have a normal probability distribution with mean 40 and standard deviation 10

Questions

What is the probability distribution of the stock price at the end of 2 years? ½ years? ¼ years? Dt years?