About 4% of the scientists in the National Academy of Sciences believe in PSl (p

Question

About 4% of the scientists in the National Academy of Sciences believe in PSl (parapsychology such as psychokinesis, telepathy, and astral projection). At a convention 173 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 173 and p 0.04. (a) How many scientists at the convention do you expect do believe in (b) What are the chances that none of the scientists at the convention believes in PSI? (c) What are the chances that at least 4 scientists at the convention believe in PSI? (d) What is the standard deviation of X? Check

Explanation / Answer

a) Scientists expected = 173*0.04 = 6.92

b) P(X = 0) = (1-0.04)^173 = 0.000857

c) P(X>=4) = 0.918267

d) Standard Deviation = SQRT(173*0.04*0.96) = 2.577

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