Below, we assume that for a random variable Z with Z N (0, 1), the stock price St at time t satisfies ln(St/S0) = ( (1/2)^2)t+tZ. Suppose that S0 = 50, = 0.08, = 0.02, and = 0.3. 1.a. Find the numerical value of a real number x such that the probability of the event that after exactly 6 months, the stock price is 60, is equal to N(x) (do not try to find the numerical value of N(x)). Use three decimals in your answer. Show your work. b. Find the numerical value of a real number x such that the probability of the event that after exactly 3 months, the stock price is 55, is equal to N(x) (do not try to find the numerical value of N(x)). Use three decimals in your answer. Show your work. c. Find the numerical value of a real number x such that the probability of the event that after exactly 3 months, the stock price is 40, is equal to N(x) (do not try to find the numerical value of N(x)).