This paper derives, in closed forms, upper and lower bounds on risk-neutral cumulative distribution functions of the underlying asset price from the observed prices of European call options, based only on the no-arbitrage assumption. The computed bounds from real data show that the gap between the upper and lower bounds is large near the underlying asset price but gets smaller away from the underlying asset price. Since the bounds can be easily computed and visualized, they could be practically used by investors in various ways.