137 Pesticides on food samples. The Food and Drug Administration (FDA) produces a quarterly report called Total Diet Study . The FDA’s report covers more than 200 food items, each of which is analyzed for dangerous chemical compounds. One Total Diet Study reported that no pesticides at all were found in 65% of the domestically produced food samples. Consider a random sample of 800 food items analyzed for the presence of pesticides.

a. Compute m and s for the random variable x , the number of food items found without any trace of pesticide.

b. On the basis of a sample of 800 food items, is it likely that you would observe fewer than half without any traces of pesticide? Explain.