Assume the Black-Scholes framework. Let S(t) denote the time-t price of a nondividend-paying stock. You are given: 

(i) The current stock price is 38. 

(ii) The stock’s volatility is 35%. 

(iii) The continuously compounded expected return on the stock is 16%

(iv) The continuously compounded risk-free interest rate is 5%.

Determine the probability distribution of S(0.5).