Problem 4

A factory cans fresh pineapple in sugar syrup. The manager in charge is interested in estimating the average amount of sugar per can to within 3 mg of the true mean. From previous experiments, based on a very large sample, he knows that the standard deviation of the sugar content is approximately 5 mg. Each test of measuring the amount of sugar in a can costs $ 27. One thousand dollars have been budgeted for this experiment. Does the manager have enough funds to estimate the average amount of sugar per can with a 92 percent confidence?

Problem 5

A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus, and 8% of the time if the person does not have the virus. If a person tests positive, determine the probability that the person is infected.