PLEASE ANSWER #5 ONLY! I am confused on how to use normalcdf to find the final answer here, using Black-Scholes theorem

finance/statistics

Suppose the current price of a share of stock is $100 and that it will change to either $50, $175, or $200 in the future. Let $c be the price to buy a unit of an option to buy a share of the stock for $150 in the future. Let P, and P2 be the probabilities respectively that the stock price is $50 and $175 in the future. Find the risk-free probabilities in terms of c, and find the values of c that an arbitrage opportunity exists. The current price of a stock is $50 and we assume it can be modeled by geometric Brownian motion with 0 .15. If the interest rate is 5% and we want to sell an option to buy the stock for $55 in 2 years, what should be the price of the option for there not to be an arbitrage opportunity? 5