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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
where λ = μ
for P(X=0) we have 6.73×10⁻³
P(X=1) we have 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 0.1755
P(X=5) we have 0.1755
P(X=6) we have 0.14622
Therefore P(X=4) or P(X=5), P(X=6) is given by
0.1755 + 0.17546 + 0.14622 = 0.49716