Consumer Reports found widespread contamination of seafood in New York and Chicago supermarkets. For example, 40% of the swordfish pieces available for sale have a level of mercury above the Food and Drug Administration (FDA) limit. Consider a random sample of 20 swordfish pieces from New York and Chicago supermarkets.
a. Use the normal approximation to the binomial to calculate the probability that fewer than 2 of the 20 swordfish pieces have mercury levels exceeding the FDA limit.
b. Use the normal approximation to the binomial to calculate the probability that more than half of the 20 swordfish pieces have mercury levels exceeding the FDA limit.
c. Use the binomial tables to calculate the exact probabilities in parts a and b. Does the normal distribution provide a good approximation to the binomial distribution?