The manager of the quality assurance department of a light bulb manufacturing company, based on his experience, claims that 96%of the bulbs manufactured by the company are defect free. The CEO of the company, a quality-conscious person, checks a random sample of 225 bulbs and finds only 87% percent of the bulbs to be defect-free.1) Please find the 95% confidence interval for the sample value. 2) Is 96% (defect rate) within the confidence interval you calculated?

PLEASE SHOW FORMULA AND ALL CALCULATIONS