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 0 1 2 3 4 5-9 10+ Total 1,983 576 136 148 91 138 38,820 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 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 ( require dentures under these altered assumptions? (Hint: Consider a mixture of two Poisson distributions.)
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 0 1 2 3 4 5-9 10+ Total 1,983 576 136 148 91 138 38,820 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 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 ( require dentures under these altered assumptions? (Hint: Consider a mixture of two Poisson distributions.)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.CR: Chapter 7 Review
Problem 88CR
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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
0
1
2
3
4
5-9
10+
Total
Frequency
35,748
1,983
576
136
148
91
138
38,820
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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