You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 381 randomly selected caterpillars observed, 50 lived to...

You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 381 randomly selected caterpillars observed, 50 lived to become butterflies. Round answers to 4 decimal places where possible.

a. With 90% confidence the proportion of all caterpillars that lived to become a butterfly is between ______and ______ .

b. If many groups of 381 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.