Find the probability ????
2011-11-23 2:46 am
It is known that the number of bacteria of a certain kind per cm3 of sea water follows a Poisson distribution with mean 3. (a) Find the probability that a sample of 1 cm3 of sea water of contains exactly 2 bacteria.(b) Find the probability that a sample of 1 cm3 of sea water of contains at least 3 bacteria.(c) If 5 samples of 1 cm3 of sea water are taken, find the probability that 3 of them contain exactly 2 bacteria
回答 (1)
2011-11-24 2:04 am
✔ 最佳答案
(a) mean =3P(x=2)=e^-3 (3^2/2!)
P(x=2)=e^-3(9/2)
P(x=2)=0.224 (corr to 3 sig. fig.)
(b) 1-P(x<3)=1-e^-3(3^0/0!+3^1/1!+3^2/2!)
=1- e^-3(1+3+9/2)
=1-0.423
=0.577
(c) P(x=2)=0.224
P(x<>2)=1-0.224=0.776
5C3*(0.224)^3*(1-0.224)^2
=10*(0.00677)
=0.0677 (corr to 3 sig. fig.)
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