The construction time for a bridge depends on weather conditions. The project is expected to take 250 days if the weather is dry and the temperature is hot. If the weather is damp and cool, the project is expected to take 350 days. Otherwise, it is expected to take 300 days. Historical data suggest that the probability of cool, damp weather is 30% and that of dry, hot weather is 20%. Find the project's probability distribution and expected completion time.