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 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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