An article presents a new method for timing traffic signals in heavily traveled intersections. The effectiveness of the new method was evaluated in a simulation study. In 50 simulations, the mean improvement in traffic flow in a particular intersection was 654.1 vehicles per hour, with a standard deviation of 311.7 vehicles per hour. a) Approximately what sample size is needed so that a 95% confidence interval will specify the mean to within 50 vehicles per hour? (Round the final answer to the nearest whole number.The sample size is. b) Find a 98% confidence interval for the improvement in traffic flow due to the new system. (Round the final answers to three decimal places.) The 98% confidence interval is ().