214 CHAPTER 5 Discrete Probability Distributions Statistical Literacy and Critical Thinking 1.Random Variable The accompanying table lists probabilities for the corresponding numbers of unlicensed software packages when four software packages are randomly selected in China. What is the random variable, what are its possible values, and are its values numerical? Number of Unlicensed Software Packages x P(x) 0 0.008 1 0.076 2 0.265 3 0.412 4 0.240 2.Discrete or Continuous? Is the random variable given in the table from Exercise 1 discrete or continuous? Explain. 3. Probability Distribution For the table from Exercise 1, is the sum of the values of P1x2 equal to 1, as required for a probability distribution? Does the table describe a probability distribution? 4. Significant For 100 births, P(exactly 56 girls) = 0.0390 and P(56 or more girls) = 0.136. Is 56 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question? Identifying Discrete and Continuous Random Variables. In Exercises 5 and 6, refer to the given values, then identify which of the following is most appropriate: discrete random variable, continuous random variable, or not a random variable. 5. a. IQ scores of statistics students b. Exact heights of statistics students c. Shoe sizes (such as 8 or 8½) of statistics students d. Majors (such as history) of statistics students e. The number of rolls of a die required for a statistics student to get the number 4 6.a. Numbers of students in statistics classes b. Grades (A, B, C, D, F) earned in statistics classes c. Number of times a statistic student must draw a card from a shuffled deck before getting an ace d. Social Security numbers of statistics students e. Exact unrounded ages of statistics students Identifying Probability Distributions. In Exercises 7–14, determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. 7.Plane Crashes The table lists causes of fatal plane crashes with their corresponding probabilities. 5-1 Basic Skills and Concepts Cause Probability Pilot Error 0.58 Mechanical 0.17 Weather 0.06 Sabotage 0.09 Other 0.10
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