Question 1024221: In a recent survey, 73% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, a) find the probability that exactly 8 of them favor the building of the police substation. b) less than 3 of them favor the building of the police substation.
Answer by mathmate(429)   (Show Source):
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Question:
In a recent survey, 73% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, a) find the probability that exactly 8 of them favor the building of the police substation. b) less than 3 of them favor the building of the police substation.
Solution:
Assuming the surveyed 73% still holds, and that the population is large enough such that 14 is a relatively small fraction of the population, and that the 14 subjects are randomly and independently chosen, then we can apply the binomial distribution, with parameters n=14, p=0.73.
(a) 8 in favour out of random sample of 14
P(X=8;14;0.73)=C(14,8)*0.73^8*(1-0.73)^(14-8)
=3003*0.08065*0.0003874
=0.09383
(b) less than 3 in favour out of 14
P(0≤X≤2; 14, 0.73)
= P(0)+P(1)+P(2)
= 1.09419^-08 + 4.141711^-07 + 7.278674^-06
= 7.703787^(-06)
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