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CHAPTER2Probability Concepts and ApplicationsTEACHING SUGGESTIONSTeaching Suggestion 2.1:Concept of Probabilities Ranging From 0 to 1.People often misuse probabilities by such statements as, “I’m 110% sure we’re going to win thebig game.” The two basic rules of probability should be stressed.Teaching Suggestion 2.2:Where Do Probabilities Come From?Students need to understand where probabilities come from. Sometimes they are subjective andbased on personal experiences. Other times they are objectively based on logical observationssuch as the roll of a die. Often, probabilities are derived from historical data—ifwe can assumethe future will be about the same as the past.Teaching Suggestion 2.3:Confusion Over Mutually Exclusive and Collectively Exhaustive Events.This concept is often foggy to even the best of students—even if they just completed a course instatistics. Use practical examples and drills to force the point home. The table at the end ofExample 3 is especially useful.Teaching Suggestion 2.4:Addition of Events That Are Not Mutually Exclusive.The formula for adding events that are not mutually exclusive is P(Aor B) = P(A) + P(B) – P(Aand B). Students must understand why we subtract P(Aand B). Explain that the intersect hasbeen counted twice.Teaching Suggestion 2.5:Statistical Dependence with Visual Examples.Figure 2.3 indicates that an urn contains 10 balls. This example works well to explain conditionalprobability of dependent events. An even better idea is to bring 10 golf balls to class. Six shouldbe white and 4 orange (yellow). Mark a big letter or number on each to correspond to Figure 2.3and draw the balls from a clear bowl to make the point. You can also use the props to stress howrandom sampling expects previous draws to be replaced.Teaching Suggestion 2.6:Concept of Random Variables.Students often have problems understanding the concept of random variables. Instructors need totake this abstract idea and provide several examples to drive home the point. Table 2.4 has someuseful examples of both discrete and continuous random variables.2-1
Teaching Suggestion 2.7:Expected Value of a Probability Distribution.A probability distribution is often described by its mean and variance. These important termsshould be discussed with such practical examples as heights or weights of students. But studentsneed to be reminded that even if most of the men in class (or the United States) have heightsbetween 5 feet 6 inches and 6 feet 2 inches, there is still some small probability of outliers.Teaching Suggestion 2.8:Bell-Shaped Curve.Stress how important the normal distribution is to a large number of processes in our lives (forexample, filling boxes of cereal with 32 ounces of cornflakes). Each normal distribution dependson the mean and standard deviation. Discuss Figures 2.8 and 2.9 to show how these relate to theshape and position of a normal distribution.