You are interested in constructing a 95% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 415 randomly selected caterpillars observed, 55 lived to become butteries. Round answers to 4 decimal places where possible. a. With 95% confidence the proportion of all caterpillars that lived to become a butterfly is between C] and C]. b. If many groups of 415 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About:] percent of these confidence intervals will contain the true population proportion of caterpillars that become butteries and about C] percent will not contain the true population proportion