Glyptapanteles is a genus of parasitic wasp found in Central America, North America, and New Zealand. The female wasps deposit their eggs into the bodies of caterpillars, where the larvae take over the

caterpillar's body as their host and the caterpillar eventually dies. While this sounds particularly morbid, the USDA has investigated the use of glyptapanteles as a biocontrol agent against caterpillars of the invasive

gypsy moth population. Suppose the USDA wants to conduct a study to investigate the proportion of gypsy moth caterpillars which can be killed by the introduction of glyptapanteles. Find the sample size needed to estimate a 99% confidence interval for the true proportion of gypsy moth caterpillars killed within 3%.