SOLUTION: About 4% of the scientists in the National Academy of Sciences believe in PSI (parapsychology such as psychokinesis, telepathy, and astral projection). At a convention 107 members

Question 859938: About 4% of the scientists in the National Academy of Sciences believe in PSI (parapsychology such as psychokinesis, telepathy, and astral projection). At a convention 107 members show up. Let X be the number of scientists at the convention who believe in PSI. You may assume for the following questions that X is binomially distributed with parameters n=107 and p=0.04.
(a) How many scientists at the convention do you expect do believe in PSI? Answer
(b) What are the chances that none of the scientists at the convention believes in PSI? Answer
(c) What are the chances that at least 4 scientists at the convention believe in PSI? Answer
(d) What is the standard deviation of X
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
About 4% of the scientists in the National Academy of Sciences believe in PSI (parapsychology such as psychokinesis, telepathy, and astral projection). At a convention 107 members show up. Let X be the number of scientists at the convention who believe in PSI. You may assume for the following questions that X is binomially distributed with parameters n=107 and p=0.04.
(a) How many scientists at the convention do you expect to believe in PSI? Answer:: np = 107*0.04 = 4.28
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(b) What are the chances that none of the scientists at the convention believes in PSI? Answer P(x = 0) = 0.96^107 = 0.0127
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(c) What are the chances that at least 4 scientists at the convention believe in PSI? Answer:: P(4<= x <=107) = 1-P(0<=x<=3)
= 1-binomcdf(107,0.04,3) = 0.6240
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(d) What is the standard deviation of X
std = sqrt(npq) = sqrt(107*0.04*0.96) = 2.0270
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Cheers,
Stan H.
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