I want to solve the following question: Let $X(t)$ be the price of JetCo stock at time $t$ years from the present. Assume that $X(t)$ is a geometric Brownian motion with zero drift and volatility $\sigma = 0.4/yr$. If the current price of JetCo stock is 8.00 USD, what is the probability that the price will be at least 8.40 USD six months from now.
Here is my attempt: Since $X(t)$ is a geometric Brownian motion, $\log(X(t))$ is a regular Brownian motion with zero drift and $\sigma = 0.4 / yr$. We want to find the probability that $\log(X(1/2)) \geq \log(8.40)$ given that $\log(X(0))= \log(8.00)$.
What can I do from here?