P336. 7. The capacities ( in ampere-hours) were measured for a sample of 120 batteries. The average was 178 and the standard deviation was 14. (a) Find a 95% confidence interval for the mean capacity of batteries produced by this method. (b) Find a 99% confidence interval for the mean capacity of batteries produced by this method. (c) An engineer claims that the mean capacity is between 176 and 180 ampere-hours. With what level of confidence can this statement be made? (d) Approximately how many batteries must be sampled so that a 95% confidence interval will specify the mean to within ±2 ampere-hours? (e) Approximately how many batteries must be sampled so that a 99% confidence interval will specify the mean to within ±2 ampere-hours?