You are interested in constructing a 99% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 357 randomly selected caterpillars observed, 48 lived to...

You are interested in constructing a 99% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 357 randomly selected caterpillars observed, 48 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 357 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 butterflies and about  percent will not contain the true population proportion.