The Foraging Capability of Downy Woodpeckers Can Be Compromised If

The foraging capability of Downy Woodpeckers can be compromised if part of their habitat disappears due to significant human encroachment. These creatures eat insects in trees, and if they cannot find enough food due to a decreasing forest area their body mass may decrease. A 20-year-old study of Downy Woodpeckers indicates that for male Downy Woodpeckers the average mass is about 28g, with a standard deviation of approximately 1.5g. Suppose it is desired to estimate μ, the average mass of male Downy Woodpeckers in a local forest preserve. If the 20-year-old values are taken as reasonable estimates, determine the sample size necessary to estimate μ to within 0.2 grams with 95% confidence.