You are interested in constructing a 95% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 364 randomly selected caterpillars observed, 56 lived to become butterflies. 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 (_________ )and (_________) .

b. If many groups of 364 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.