Respuesta :
Answer:
The answers to the question are
a) The probability that at most 1 person suffers side effect from the flu vaccine is 4.043×10⁻²
b) The probability that 4,5,or 6 persons suffer side effect from the flu vaccine is 0.49716.
Step-by-step explanation:
We solve the question using the formula for Poisson probability as follows
Let the probability of suffering a side effect from a certain flu vaccine be p
we have n = 1000 and p = 0.005
then by binomial theorem μ = 1000*0.005 = 5
using Poisson probability formula, we have[tex]P(X=k) =\frac{\lambda ^k e^{-\lambda}}{k!}[/tex]
where λ = μ
for P(X=0) we have [tex]\frac{5^0e^{-5}}{0!} =[/tex] 6.73×10⁻³
P(X=1) we have [tex]\frac{5^1e^{-5}}{1!} =[/tex] 3.37×10⁻²
Using the addition rule, we have
P (X≤1) = P(X=0) + P(X=1) = 6.73×10⁻³ + 3.37×10⁻² = 4.043×10⁻²
b) Similarly, we have for k = 4, 5, 6 we have
P(X=4) we have [tex]\frac{5^4e^{-5}}{4!} =[/tex]0.1755
P(X=5) we have [tex]\frac{5^5e^{-5}}{5!} =[/tex] 0.1755
P(X=6) we have [tex]\frac{5^6e^{-5}}{6!} =[/tex]0.14622
Therefore P(X=4) or P(X=5), P(X=6) is given by
0.1755 + 0.17546 + 0.14622 = 0.49716
