(14.40) Whooping cough (pertussis) is a highly contagious bacterial infection th

Question

(14.40) Whooping cough (pertussis) is a highly contagious bacterial infection that was a major cause of childhood deaths before the development of vaccines. About 80% of unvaccinated children who are exposed to whooping cough will develop the infection, as opposed to only about 5% of vaccinated children. The following exercise is based on this information. A group of 20 children at a nursery school are exposed to whooping cough by playing with an infected child. Of these children 17 have been vaccinated and 3 have not.

Step 1: What is the distribution of the number of new infections among the 17 vaccinated children? Normal with = 2.4 and = 0.69. Binomial with n = 17 and p = 0.8. Binomial with n = 17 and p = 0.05. Binomial with n = 3 and p = 0.8. Binomial with n = 3 and p = 0.05.

Step 2: What is the mean number of new infections among the vaccinated children? Give your answer to 2 decimal place.

Step 3: What is the distribution of the number of new infections among the 3 unvaccinated children? Normal with = 2.4 and = 0.69. Binomial with n = 17 and p = 0.8. Binomial with n = 3 and p = 0.05. Binomial with n = 3 and p = 0.8. Binomial with n = 17 and p = 0.05.

Step 4: What is the mean number of new infections among the unvaccinated children? Give your answer to 1 decimal place.

Step 5: Add your means from parts (2) and (4). This is the mean number of new infections among all 20 exposed children. Give your answer to 2 decimal places.

Explanation / Answer

1)Binomial with n = 17 and p = 0.05.

2)mean =np=17*0.05=0.85

3)Binomial with n = 3 and p = 0.8.

4)mean number =np=3*0.8=2.4

5) mean number =0.85+2.4=3.25

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