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Infectious Disease Commonly used vaccines for influenza are trivalent and contain only one type of influenza B virus. They may be ineffective against other types of influenza virus. A randomized clinical trial was performed among children 3 to 8 years of age in 8 countries. Children received either a quadrivalent vaccine (QIV) that had more than one influenza B virus or a trivalent Hepatitis A vaccine (control). An attack rate (i.e.,% of children who developed influenza) starting 14 days after vaccination until the end of the study was computed for each vaccine group, stratified by age. The following data were reported. age QIV group Control group 3-4 3.79 5.66 5-8 1.75 5.16 (a) Suppose 3 children in a village ages 3, 5, and 7 are vaccinated with the QIV vaccine. What is the probability that at least one child among the 3 will get influenza? (Round your answer to four decimal places.) (b) Suppose that 80% of 3-4-year-old children and 70% of 5-8-year-old children in a village are vaccinated with QIV vaccine. Also assume that children who are not vaccinated have twice the incidence of influenza as the control group in the table above. (Round your answers to two decimal places.) (i) What percentage of 3-4-year-old children in the village will get influenza? % (ii) What percentage of 5-8-year-old children in the village will get influenza? % (c) Suppose we identify a 5-8-year-old child with influenza in the village but are uncertain whether the child was vaccinated. If we make the same assumptions that we made in part (b), then what is the probability that the child was vaccinated? (Hint: Use Bayes' rule here. Round your answer to four decimal places.)

Infectious Disease Commonly used vaccines for influenza are trivalent and contain only one type of influenza B virus. They may be ineffective against other types of influenza virus. A randomized clinical trial was performed among children 3 to 8 years of age in 8 countries. Children received either a quadrivalent vaccine (QIV) that had more than one influenza B virus or a trivalent Hepatitis A vaccine (control). An attack rate (i.e.,% of children who developed influenza) starting 14 days after vaccination until the end of the study was computed for each vaccine group, stratified by age. The following data were reported. age QIV group Control group 3-4 3.79 5.66 5-8 1.75 5.16 (a) Suppose 3 children in a village ages 3, 5, and 7 are vaccinated with the QIV vaccine. What is the probability that at least one child among the 3 will get influenza? (Round your answer to four decimal places.) (b) Suppose that 80% of 3-4-year-old children and 70% of 5-8-year-old children in a village are vaccinated with QIV vaccine. Also assume that children who are not vaccinated have twice the incidence of influenza as the control group in the table above. (Round your answers to two decimal places.) (i) What percentage of 3-4-year-old children in the village will get influenza? % (ii) What percentage of 5-8-year-old children in the village will get influenza? % (c) Suppose we identify a 5-8-year-old child with influenza in the village but are uncertain whether the child was vaccinated. If we make the same assumptions that we made in part (b), then what is the probability that the child was vaccinated? (Hint: Use Bayes' rule here. Round your answer to four decimal places.)

Calculus For The Life Sciences
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.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Infectious Disease Commonly used vaccines for influenza are trivalent and contain only one type of influenza B virus. They may be ineffective against other types of influenza B virus. A randomized clinical trial was performed among children 3 to 8 years of age in 8 countries. Children received either a quadrivalent vaccine (QIV) that had more than one influenza B virus or a trivalent Hepatitis A vaccine (control). An attack rate (i.e.,% of children who developed influenza) starting 14 days after vaccination until the end of the study was computed for each vaccine group, stratified by age. The following data were reported. age QIV group Control group 3-4 3.79 5.66 5-8 1.75 5.16 (a) Suppose 3 children in a village ages 3, 5, and 7 are vaccinated with the QIV vaccine. What is the probability that at least one child among the 3 will get influenza? (Round your answer to four decimal places.) (b) Suppose that 80% of 3-4-year-old children and 70% of 5-8-year-old children in a village are vaccinated with QIV vaccine. Also assume that children who are not vaccinated have twice the incidence of influenza as the control group in the table above. (Round your answers to two decimal places.) (i) What percentage of 3-4-year-old children in the village will get influenza? % (ii) What percentage of 5-8-year-old children in the village will get influenza? % (c) Suppose we identify a 5-8-year-old child with influenza in the village but are uncertain whether the child was vaccinated. If we make the same assumptions that we made in part (b), then what is the probability that the child was vaccinated? (Hint: Use Bayes' rule here. Round your answer to four decimal places.)
Transcribed Image Text:Infectious Disease Commonly used vaccines for influenza are trivalent and contain only one type of influenza B virus. They may be ineffective against other types of influenza B virus. A randomized clinical trial was performed among children 3 to 8 years of age in 8 countries. Children received either a quadrivalent vaccine (QIV) that had more than one influenza B virus or a trivalent Hepatitis A vaccine (control). An attack rate (i.e.,% of children who developed influenza) starting 14 days after vaccination until the end of the study was computed for each vaccine group, stratified by age. The following data were reported. age QIV group Control group 3-4 3.79 5.66 5-8 1.75 5.16 (a) Suppose 3 children in a village ages 3, 5, and 7 are vaccinated with the QIV vaccine. What is the probability that at least one child among the 3 will get influenza? (Round your answer to four decimal places.) (b) Suppose that 80% of 3-4-year-old children and 70% of 5-8-year-old children in a village are vaccinated with QIV vaccine. Also assume that children who are not vaccinated have twice the incidence of influenza as the control group in the table above. (Round your answers to two decimal places.) (i) What percentage of 3-4-year-old children in the village will get influenza? % (ii) What percentage of 5-8-year-old children in the village will get influenza? % (c) Suppose we identify a 5-8-year-old child with influenza in the village but are uncertain whether the child was vaccinated. If we make the same assumptions that we made in part (b), then what is the probability that the child was vaccinated? (Hint: Use Bayes' rule here. Round your answer to four decimal places.)
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