The manufacturer of the colorsmart-5000 television set claims 95 percent of its sets last at least five years without needing a single repair. in order to test this claim, a consumer group randomly selects 444 consumers who have owned a colorsmart-5000 television set for five years. of these 444 consumers, 316 say their colorsmart-5000 television sets did not need a repair, whereas 128 say their colorsmart-5000 television sets did need at least one repair.

(a) find a 99 percent confidence interval for the proportion of all colorsmart-5000 television sets that have lasted at least five years without needing a single repair. (round your answers to 3 decimal places.)