1. 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 sample of 40 bulbs. The average lifetime of these 40 bulbs was 740 hours with hours. The manufacturer responded that its claim was 푠=30based on testing hundreds of bulbs. a.If the consumer group and manufacturer both make 95% confidence intervals for the population’s average lifetime, whose will probably be shorter?Can you tell for certain?b. Given the usual sampling assumptions, is there a 95% probability that 750 lies in the 95% confidence interval of the manufacturer?