2. You work for a polling company employed by a cellphone manufacturer. The manufacturer would like to find the preference of consumers about the battery life of cellphones. You know (from a previous pilot study) that the population standard deviation is 10 hours. You would like to construct a 95-percent confidence interval for the average desired battery duration. Increasing battery life is costly, so the manufacturer would like to have an estimate as precise as possible. Therefore, you want this confidence interval to be no wider than 1 (i.e., the difference between the upper and lower bound should be equal to 1). How large of a sample do you need? Explain how you would determine the sample size.