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 a95%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?