189 Where You’ve Been In Chapters 1 through 3, you learned how to collect and describe data and how to find the probability of an event. These skills are used in many different types of careers. For instance, data about climatic conditions are used to analyze and forecast the weather throughout the world. On a typical day, meteorologists use data from aircraft, National Weather Service cooperative observers, radar, remote sensing systems, satellites, ships, weather balloons, and a variety of other data-collection devices to forecast the weather. Even with this much data, meteorologists cannot forecast the weather with certainty. Instead, they assign probabilities to certain weather conditions. For instance, a meteorologist might determine that there is a 40% chance of rain (based on the relative frequency of rain under similar weather conditions). Where You’re Going In Chapter 4, you will learn how to create and use probability distributions. Knowing the shape, center, and variability of a probability distribution enables you to make decisions in inferential statistics. For example, consider a meteorologist working on a three-day forecast. Assuming that having rain on one day is independent of having rain on another day, the meteorologist determines that there is a 40% probability of rain (and a 60% probability of no rain) on each of the three days. What is the probability that it will rain on 0, 1, 2, or 3 of the days? To answer this, you can create a probability distribution for the possible outcomes. Using the Multiplication and Addition Rules with the probabilities in the tree diagram, you can determine the probabilities of having rain on various numbers of days.You can then use this information to construct and graph a probability distribution. P( , , )=0.216 P( , , )=0.144 P( , , )=0.144 P( , , )=0.096 P( , , )=0.096 P( , , )=0.096 P( , , ) = 0.144 P( , , )=0.064 0 0.6 1 1 2 2 2 1 3 Day 1 Day 2 Day 3 Probability Days of Rain 0.6 0.6 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0 Days of rain 1 2 3 Probability Number of Days of Rain x P(x) Probability Distribution Days of rain Tally Probability 0 1 0.216 1 3 0.432 2 3 0.288 3 1 0.064
RkJQdWJsaXNoZXIy NjM5ODQ=