About 4 % of the scientists in the national academy of sciences believe in PSI (

Question

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 118 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 = 118 and P = 0.04. (a) How many scientists at the convention do you expect do believe in PSI? (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?

Explanation / Answer

a. Here it is given that n=118 and p=0.04

Here it is given that assume binomial distribution

So Expected value = np=118*0.04=4.72

b. Now we know P(x)=ncxp^x(1-p)^n-x

We need to find P(x=0)=nco(0.04)^0(1-0.04)^118=0.0081

c. P(x>=4)=P(x=4,5,6,....118)=0.6989

d. Standard deviation of binomial distribution is sqrt(np1)=sqrt(118*0.04*0.96)=2.13

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