do not use normal approximation 80% of unvaccinated children who are exposed to
ID: 2918509 • Letter: D
Question
do not use normal approximation 80% of unvaccinated children who are exposed to whooping coughwill develop the infection, as opposed to only about 5 % ofvaccinated children. a group of 20 children at a nursery school are expoed towhooping cough by playing with an infected child. of thse children17 have been vaccinated and 3 have not. a. what is the distrubtion of the number of new infectionsamong the 17 vaccinated children? what is the mean number of newinfections. b. what is the distribution of the number of new infectionsamong the 3 unvaccinated children? what is the mean number of newinfections. do not use normal approximation 80% of unvaccinated children who are exposed to whooping coughwill develop the infection, as opposed to only about 5 % ofvaccinated children. a group of 20 children at a nursery school are expoed towhooping cough by playing with an infected child. of thse children17 have been vaccinated and 3 have not. a. what is the distrubtion of the number of new infectionsamong the 17 vaccinated children? what is the mean number of newinfections. b. what is the distribution of the number of new infectionsamong the 3 unvaccinated children? what is the mean number of newinfections.Explanation / Answer
a) The distribution of new infectionsamong 17 vaccinated is binomial with
P(x=k) = nck pk * (1-p)(n-k) where n = 17 and p = 0.05 and k is the number of newinfections.
Mean = np = 17*0.05 = 0.85 (this can be non integer also )
b)
The distribution of new infections among 3 unvaccinated isbinomial with
P(x=k) = nck pk * (1-p)(n-k) where n = 3 and p = 0.8 and k is the number of newinfections.
Mean = np = 3*0.8 = 2.4 (this can be non integer also )
Hope this helps. Feel free to ask for any clarifications
b) Since none are vaccinated n = 20 and p = 0.8 and 1-p =0.2
mean infections = 20*0.8 = 16.
P(x>=18) = P(x=18)+P(x=19)+P(x=20)
= 20C18 *0.22 * 0.818 +20C19 *0.21 * 0.819+20C20 *0.20 * 0.820 =20.68%
Hope it helps .Feel free to ask for any clarifications
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