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The data in the table below were reported by men in a health follow-up study on the number of teeth lost over a 1-year period (January 1, 1987, to December 31, 1987). (Round your answers to four decimal places.) Number of teeth lost Frequency 35,748 1,983 2 606 3 166 4 168 5-9 101 10+ 158 Total 38,930 You may need to use the appropriate technology to answer this question. (a) If we assume the average number of teeth lost in the 5-9 group is 7 teeth and the average number of teeth lost in the 10+ group is 12 teeth, what is the best estimate of the average number of teeth lost per y

The data in the table below were reported by men in a health follow-up study on the number of teeth lost over a 1-year period (January 1, 1987, to December 31, 1987). (Round your answers to four decimal places.) Number of teeth lost Frequency 35,748 1,983 2 606 3 166 4 168 5-9 101 10+ 158 Total 38,930 You may need to use the appropriate technology to answer this question. (a) If we assume the average number of teeth lost in the 5-9 group is 7 teeth and the average number of teeth lost in the 10+ group is 12 teeth, what is the best estimate of the average number of teeth lost per y

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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Dentistry The data in the table below were reported by men in a health follow-up study on the number of teeth lost over a 1-year period (January 1, 1987, to December 31, 1987). (Round your answers to four decimal places.) Number of teeth lost Frequency 35,748 1 1,983 2 606 3 166 4 168 5-9 101 10+ 158 Total 38,930 You may need to use the appropriate technology to answer this question. (a) If we assume the average number of teeth lost in the 5-9 group is 7 teeth and the average number of teeth lost in the 10+ group is 12 teeth, what is the best estimate of the average number of teeth lost per year? (b) Suppose that on January 1, 1987, a man is 50 years old, that he will live for 30 more years (until 2016), and that the rate of tooth loss over this 30-year period is the same as in 1987. If a man has 13 teeth remaining on January 1, 1987, what is the probability he will need dentures (have 10 or fewer teeth remaining) during his 30-year lifetime? (Hint: Use the Poisson distribution.) (c) Suppose dental practice improves over the 30-year period. We assume the rate of tooth loss per year from 1987-2001 (15 years) is the same as in 1987, whereas the rate of tooth loss per year from 2002-2016 (15 years) is half the 1987 rate. What is the probability that the man in part (b) will require dentures under these altered assumptions? (Hint: Consider a mixture of two Poisson distributions.)
Transcribed Image Text:Dentistry The data in the table below were reported by men in a health follow-up study on the number of teeth lost over a 1-year period (January 1, 1987, to December 31, 1987). (Round your answers to four decimal places.) Number of teeth lost Frequency 35,748 1 1,983 2 606 3 166 4 168 5-9 101 10+ 158 Total 38,930 You may need to use the appropriate technology to answer this question. (a) If we assume the average number of teeth lost in the 5-9 group is 7 teeth and the average number of teeth lost in the 10+ group is 12 teeth, what is the best estimate of the average number of teeth lost per year? (b) Suppose that on January 1, 1987, a man is 50 years old, that he will live for 30 more years (until 2016), and that the rate of tooth loss over this 30-year period is the same as in 1987. If a man has 13 teeth remaining on January 1, 1987, what is the probability he will need dentures (have 10 or fewer teeth remaining) during his 30-year lifetime? (Hint: Use the Poisson distribution.) (c) Suppose dental practice improves over the 30-year period. We assume the rate of tooth loss per year from 1987-2001 (15 years) is the same as in 1987, whereas the rate of tooth loss per year from 2002-2016 (15 years) is half the 1987 rate. What is the probability that the man in part (b) will require dentures under these altered assumptions? (Hint: Consider a mixture of two Poisson distributions.)
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