202 CHAPTER 4 Probability 4. Out-of-class activity Marine biologists often use the capture-recapture method as a way to estimate the size of a population, such as the number of fish in a lake. This method involves capturing a sample from the population, tagging each member in the sample, then returning it to the population. A second sample is later captured, and the tagged members are counted along with the total size of this second sample. The results can be used to estimate the size of the population. Instead of capturing real fish, simulate the procedure using some uniform collection of items such as colored beads, M&Ms, or index cards. Start with a large collection of at least 200 of such items. Collect a sample of 50 and use a marker to “tag” each one. Replace the tagged items, mix the whole population, then select a second sample and proceed to estimate the population size. Compare the result to the actual population size obtained by counting all of the items. 5. Out-of-class activity Divide into groups of three or four. First, use subjective estimates for the probability of randomly selecting a car and getting each of these car colors: black, white, blue, red, silver, other. Then design a sampling plan for obtaining car colors through observation. Execute the sampling plan and obtain revised probabilities based on the observed results. Write a brief report of the results. 6. In-class activity The manufacturing process for a new computer integrated circuit has a yield of 1>6, meaning that 1>6 of the circuits are good and the other 5>6 are defective. Use a die to simulate this manufacturing process, and consider an outcome of 1 to be a good integrated circuit, while outcomes of 2, 3, 4, 5, or 6 represent defective integrated circuits. Find the mean number of circuits that must be manufactured to get one that is good. 7. Out-of-class activity In Cumulative Review Exercise 4, it was noted that eye colors in the United States are distributed as follows: 40% brown, 35% blue, 12% green, 7% gray, 6% hazel. That distribution can form the basis for probabilities. Conduct a survey by asking fellow students to identify the color of their eyes. Does the probability of 0.4 for brown eyes appear to be consistent with your results? Why would a large sample be required to confirm that P(hazel eyes) = 0.06? 8. In-class activity Each student should survey people to determine whether they have the ability to raise one eyebrow without raising the other. All results can be combined to estimate the probability that a randomly selected person can raise one eyebrow without raising the other. 9. Out-of-class activity Have each student announce the 4th and 5th digits of their Social Security numbers. After all of those numbers have been recorded, analyze them and try to identify any features suggesting that those numbers are not random.
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