You are interested in constructing a 95% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 412 randomly selected caterpillars observed, 60 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 412 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.