198 CHAPTER 4 Discrete Probability Distributions Constructing and Graphing Discrete Probability Distributions In Exercises 19 and 20, (a) construct a probability distribution, and (b) graph the probability distribution using a histogram and describe its shape. 19. Televisions The number of high-definition (HD) televisions per household in a small town Televisions 0 1 2 3 or more Households 56 511 679 754 20. Overtime Hours The number of overtime hours worked in one week per employee Overtime hours 0 1 2 3 4 5 6 Employees 6122957423016 21. Finding Probabilities Use the probability distribution you made in Exercise 19 to find the probability of randomly selecting a household that has (a) one or two HD televisions, (b) two or more HD televisions, (c) from one to three HD televisions, and (d) at most two HD televisions. 22. Finding Probabilities Use the probability distribution you made in Exercise 20 to find the probability of randomly selecting an employee whose overtime is (a) one or two hours, (b) two hours or less, (c) from three to six hours, (d) from one to three hours, and (e) at most four hours. 23. Unusual Events In Exercise 19, would it be unusual for a household to have no HD televisions? Explain your reasoning. 24. Unusual Events In Exercise 20, would it be unusual for an employee to work two hours of overtime? Explain your reasoning. Determining a Missing Probability In Exercises 25 and 26, determine the missing probability for the probability distribution. 25. x 0 1 2 3 4 P1x2 0.06 0.12 0.18 ? 0.30 26. x 0 1 2 3 4 5 6 P1x2 0.05 ? 0.23 0.21 0.17 0.11 0.08 Identifying Probability Distributions In Exercises 27 and 28, determine whether the distribution is a probability distribution. If it is not a probability distribution, explain why. 27. x 0 1 2 3 4 P1x2 0.30 0.25 0.25 0.15 0.05 28. x 0 1 2 3 4 5 P1x2 3 4 1 10 1 20 1 25 1 50 1 100
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