if the market price of options is greater than the predicted price, should not this mean that the implied volatility is lower than the current standard deviation?
No. Option increases with volatility.
If you use 15% volatility, and calc intrinsic value as $20 while market price is 25… then market is implying higher volatility. It’s algebra! You plug in market price and solve for volatility.
standard deviation doesn’t fit in
Option what…
Option “price” you mean, I hope.
You are doing very good btw. Probably you going 150mph right now 
My question is not contradicting your answer, what I am asking about is; implied volatility (the volatility which the analyst calculates) is lower than the current standard deviation in the market and accordingly predicted price is lower than market price. Am I right!
That would mean that the implied volatility used to determine the price of the option is higher.
150mph is good but don’t want to crash.
Volatility vs standard deviations isn’t a typical comparison from a CFA test question, as far as I know.Typicslly they ask what happens to price and implied volatility.
i guess you could say standard deviation is higher with higher volatility.