Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer it takes the plane to unload and load passengers. One regional airline is considering changing its policy to allow only one carry-on per passenger. Before doing so, the airline decided to collect some data. Specifically, a random sample of 500 passengers was selected. Researchers observed the passengers and noted the number of bags each person carried on the plane. Out of the 500 passengers, 170 had more than one bag.

a. Based on this sample, develop and interpret a 98% confidence interval estimate for the proportion of the traveling population that would have been impacted had the "one-bag" limit been in effect. Discuss your result.