Problem N5613 probability theory confidence interval

5613. Selectively examined 225 electric bulbs for increased voltage. According to the sample, the average service life (in hours) of electric lamps turned out to be 200 hours. Assuming that the lamp life is normally distributed, find with a reliability of 0.99 a confidence interval for the average life of the lamps produced by the factory, knowing that the standard deviation of the lamp burning time is 30 hours.