Question 747897: It is estimated that, in jury trials, the jury will reach the correct decision
(guilty or not guilty) 92% of the time. In 200 randomly selected jury trials,
a. what is the probability that the jury will reach the correct decision in at least 175 of the trials?
b. what is the probability that there will be fewer than 180 correct decisions?
c. What is the probability that there will be exactly 184 correct decisions?
(Why does the binomial theorem give a different answer than finding the z score and looking up p in the normal table?)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! It is estimated that, in jury trials, the jury will reach the correct decisio
(guilty or not guilty) 92% of the time. In 200 randomly selected jury trials,
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Binomial with n = 200 and p(correct) = 0.92
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a. what is the probability that the jury will reach the correct decision in at least 175 of the trials?
P(x >= 175) = 1 - P(0<= x <=174) = 0.9901
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b. what is the probability that there will be fewer than 180 correct decisions?
P(0<= x <=179) = 0.1225
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c. What is the probability that there will be exactly 184 correct decisions?
P(x = 184) = binompdf(200,0.92,184) = 0.1034
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(Why does the binomial theorem give a different answer than finding the z score and looking up p in the normal table?)
The probability of ANY spedific number is zero in a continuous distribution.
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Cheers,
Stan H.
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