218 CHAPTER 4 Discrete Probability Distributions TRY IT YOURSELF 2 What is the probability that more than four accidents will occur in any given month at the intersection? Answer: Page A39 In Example 2, you used a formula to determine a Poisson probability. You can also use a table to find Poisson probabilities. Table 3 in Appendix B lists the Poisson probabilities for selected values of x and m. You can also use technology tools, such as Minitab, Excel, StatCrunch, and the TI-84 Plus, to find Poisson probabilities. Finding a Poisson Probability Using a Table A population count shows that the average number of rabbits per acre living in a field is 3.6. Use a table to find the probability that seven rabbits are found on any given acre of the field. SOLUTION A portion of Table 3 in Appendix B is shown here. Using the distribution for m = 3.6 and x = 7, you can find the Poisson probability as shown by the highlighted areas in the table. m x 3.1 3.2 3.3 3.4 3.5 3.6 3.7 0 .0450 .0408 .0369 .0334 .0302 .0273 .0247 1 .1397 .1304 .1217 .1135 .1057 .0984 .0915 2 .2165 .2087 .2008 .1929 .1850 .1771 .1692 3 .2237 .2226 .2209 .2186 .2158 .2125 .2087 4 .1734 .1781 .1823 .1858 .1888 .1912 .1931 5 .1075 .1140 .1203 .1264 .1322 .1377 .1429 6 .0555 .0608 .0662 .0716 .0771 .0826 .0881 7 .0246 .0278 .0312 .0348 .0385 .0425 .0466 8 .0095 .0111 .0129 .0148 .0169 .0191 .0215 9 .0033 .0040 .0047 .0056 .0066 .0076 .0089 10 .0010 .0013 .0016 .0019 .0023 .0028 .0033 According to the table, the probability is 0.0425. You can check this result using technology. As shown below using Excel, the probability is 0.042484. After rounding to four decimal places, the probability is 0.0425, which is the same value found using the table. EXCEL 0.042484 =POISSON(7,3.6,FALSE) A 1 Interpretation So, the probability that seven rabbits are found on any given acre is 0.0425. Because 0.0425 is less than 0.05, this can be considered an unusual event. TRY IT YOURSELF 3 Two thousand brown trout are introduced into a small lake. The lake has a volume of 20,000 cubic meters. Use a table to find the probability that three brown trout are found in any given cubic meter of the lake. Answer: Page A39 EXAMPLE 3 Picturing the World TheTacoma Narrows Bridge is a suspension bridge that spans the Tacoma Narrows in Washington State.The average occupancy of vehicles that travel across the bridge is 1.6. The probability distribution shown below represents the vehicle occupancy on the bridge during a five-day period. (Adapted from Washington State Department of Transportation) Number of people in vehicle Probability 0.60 0.40 0.80 0.20 1 2 3 4 5 6+ x P(x) During the five-day period, what is the probability that a randomly selected vehicle has two occupants or fewer?
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