You are interested in constructing a 99% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 438 randomly selected caterpillars observed, 57 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 99% confidence the proportion of all caterpillars that lived to become a butterfly is between and b. If many groups of 438 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About 99 percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about 1 percent will not contain the true population proportion