1 answer

9. [12pts: 3pts each] It is estimated that 7 centers that cannot be detected until the...

Question:

9. [12pts: 3pts each] It is estimated that 7 centers that cannot be detected until the tangerines are cut open. The of 8 What is the probability of geting at least two good tangerines in a 096 ofa tangerine crop is good; the other 30% have rotten Chace at leass z 8oos tunyes Sucx 3 What is the probability of getting less than six good tangerines in a sack? 4790 Chance of good burger Mes 309.

9. [12pts: 3pts each] It is estimated that 7 centers that cannot be detected until the tangerines are cut open. The of 8 What is the probability of geting at least two good tangerines in a 096 ofa tangerine crop is good; the other 30% have rotten Chace at leass z 8oos tunyes Sucx 3 What is the probability of getting less than six good tangerines in a sack? 4790 Chance of good burger Mes 309.

Answers

p=70\%=0.7,n=8

Let q=1-p=0.3

P(X=x)=n_{C_{x}}(q)^{n-x}(p)^{x}

a) P(X\geq 2)=1-P(X=0)-P(X=1)

=1-8_{C_{0}}(0.3)^{8-0}(0.7)^{0}-8_{C_{1}}(0.3)^{8-1}(0.7)^{1}

=1-(0.3)^{8}-8(0.3)^{7}(0.7)

=0.9987

b) P(X< 6)=1-P(X=6)-P(X=7)-P(X=8)

=1-8_{C_{6}}(0.3)^{8-6}(0.7)^{6}-8_{C_{7}}(0.3)^{8-7}(0.7)^{7} -8_{C_{8}}(0.3)^{8-8}(0.7)^{8}

  =1-28(0.3)^{2}(0.7)^{6}-8(0.3)(0.7)^{7}-(0.7)^{8}

=0.4482

.

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