Bluman 5th_Chapter 5 HW Soln - 1 Chapter 5.1 7 9 11 13 15...

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1 Chapter 5.1 # 7, 9, 11, 13, 15, 17, 19, 25, 27 For exercises 6 through 11, determine whether the distribution represents a probability distribution. If it does not, state why. 7. No, we cannot have negative numbers, and P(x) does not equal 1. 9. = 10 10 = 1, yes 1. Each P(x) is between 0 and 1. 10 ( ) 1 10 p x = = . 11. 2 1 = , No, not equal to 1. 1. P(x) = 1.2 is not between 0 and 1, 2. ( ) 2 1 p x = For Exercises 12 through 18, state whether the variable is discrete or continuous. 13. The number of cheeseburgers a fast-food restaurant serves each day. Discrete 15. The weight of a Siberian tiger. Continuous 17. The number of mathematics majors in your school. Discrete For Exercises 19 through 26, construct a probability distribution for the data and draw a graph for the distribution. 19. Medical tests the probabilities that a patient will have 0, 1, 2, or 3 medical tests performed on entering a hospital are 6 5 3 1 , , , 15 15 15 15 and respectively. X 3 6 8 12 P(x ) 0. 3 0. 5 0. 7 -0.8 X 1 2 3 4 5 P(x ) X 5 10 15 P(x ) 1. 2 0. 3 0.5
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2 25. Student Classes The probabilities that a student is registered for 2, 3, 4, or 5 classes are 0.01, 0.34, 0.62, and 0.03, respectively. 27. Selecting a Monetary Bill A box contains three $1 bills, two $5 bills, five $10 bills, and one $20 bill. Construct a probability distribution for the data if x represents the value of a single bill drawn at random and then replaced. Chapter 5.2 #3, 7, 11, 12, 13, 15, 18 3. Number of Credit Cards A bank vice president feels that each savings account customer has, on average, three credit cards. The following distribution represents the number of credit cards people won. Find the mean, variance, and standard deviation. Is the vice president correct? X P(X) 0 6/15 1 5/15 2 3/15 3 1/15
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3 Number of Credit Cards X 0 1 2 3 4 Probabili ty P(X) 0.18 0.44 0.27 0.08 0.03 Mean: 0 0.18 1 0.44 2 0.27 3 0.08 4 0.03 1 ( ) .34 X P X μ = + ⋅ + + + = = g Variance 2 2 2 ( ) X P X σ μ = - = 2 2 2 2 2 2 0 0.18 1 0.44 2 0.27 3 0.08 4 0.03 1.34 2.72 1.7956 0.9 + + + + - = - = Standard deviation 0.9 1 σ = No, the vice president is not correct. On average, each person has about one credit card.
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