Every quarter, the Food and Drug Administration (FDA) produces a report called the Total Diet Study. The FDA's report covers a variety of food items, each of which is analyzed for potentially harmful chemical compounds. A Total Diet Study reported that no pesticides at all were found in 65% of the domestically produced food samples (FDA Pesticide Program: Residue Monitoring, 2008). Consider a random sample of 800 food items analyzed for the presence of pesticides.
a. Compute μ and σ for the random variable x, the number of food items found that showed no trace of pesticide.
b. Based on a sample of 800 food items, is it likely you would observe less than half without any traces of pesticide? Explain.