A while back, Colgate claimed that "80% of dentists recommend Colgate" (this is a true story). To test this claim, a survey of 250 randomly selected dentists is conducted. Of the 250, 167 recommend using Colgate. Find a 99% confidence interval for the population proportion. Round your answer to the nearest 3 decimal places. Give an interpretation of the confidence interval in context. Do you think Colgate's claim is reasonable? Why or why not