Utilizing statistics in options and intuitive explanation

Let's say there is a 70% chance of a call option being in the money with a given volatility. I understand what it is saying but intuitively what exactly does this information tell you? Is there a way to get an expected value of the call option without using Black Scholes formula. The probability is over a certain range, but is there way to get a final output instead of a range, or do we just accept there is a formula to calculate this and that is the way it is done. Thanks. 

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