Bags of a chemical produced by a company have impurity weights that can
be represent by a normal distribution with mean 12.2 grams and standard
deviation 2.8 grams. A random sample of 400 of these bags is taken. What
is the probability that at least 100 of them contain less than 10 grams of
impurities? (10%)
Consider a fishing company on the coast of New England. It operates a
search plane to find schools of salmon that are randomly located in the
North Atlantic. On average, 1 school of salmon appears per 100,000 square
miles of sea. On a given day, the plane can fly 1,000 miles, effectively
searching a lateral distance of 5 miles on either side of its path.
(a) What is the probability of finding at least one school of salmon during 3
days of searching? (10%)
(b) How many days of search are needed before the probability of finding at
least 1 school of salmon reaches 0.95? (10%)
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