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Show all your work. Indicate clearly the methods you use because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanation.
A simple random sample of adults living in a suburb of a large city was selected. The age and annual income of each adult in the sample were recorded. The resulting data are summarized in the table below.
Age Category $25,000–$35,000 $35,001–$50,000 Over $50,000 Total
21–30 8 15 27 50
31–45 22 32 35 89
46–60 12 14 27 53
Over 60 5 3 7 15
Total 47 64 96 207
a) What is the probability that a person chosen at random from those in this sample will be in the 31–45 age category?
b) What is the probability that a person chosen at random from those in this sample whose incomes are over $50,000 will be in the 31–45 age category? Show your work.
c) Based on your answers to (a) and (b), is annual income independent of age category for those in this sample? Explain. (7 points)
10. The following table is the assignment of probabilities that describes the age (in years) and the gender of a randomly selected American student.
Age 14–17 18–24 25–34 +35
Male 0.01 0.30 0.12 0.04
Female 0.01 0.30 0.13 0.09
a) What is the probability that the student is female?
b) What is the probability that the student is age 25–34?
c) What is the probability that the student is either male or at least 35 years old?
d) What is the probability that the student is at least 35 years old?
e) Are being a female and being at least 35 years old independent events? Provide statistical reasoning for your answer. (7 points)