A package of light bulbs promises an average life of more than 750 hours per bulb. A consumer group did not believe the claim and tested a random sample of 40 bulbs. The average lifetime of these 40 bulbs was 740 hours. We can assume that σ = 30 hours. Providing this information to the manufacturer, the manufacturer responds that his claim was based on a random sample of several hundreds of bulbs.(a) [Free Response] If the consumer group and the manufacturer both construct a 95% confidence interval for the population’s true average lifetime, whose interval will be shorter? Explain.(b) [True or False] Given the usual sampling assumptions, there is a 95% chance that 740 lies in the 95% confidence interval of the manufacturer.(c) [Free Response] Assuming both parties constructed each a 95% confidence interval, is the manufacturer’s confidence interval more likely to contain the population mean because it is based on a larger sample? Explain why or why not.