Question

According to Real Clear Politics’s poll conducted in the first half of January 2015, 32% of respondents say that the country is going to the right direction while 58% of them say the country is on the wrong track, while the rest have no opinion. a. Of 30 respondents, find the expected number of respondents without opinion. b. Of 70 respondents, find the standard deviation of the number of respondents saying the country is going to the right direction. c. Find the probability that, of 8 voters, at least 5 of them say the country is on the wrong track. d. Find the probability that any of those 8 respondents has/have no opinion. e. Of 30 respondents, find the “usual” interval for the number of responding without opinion.

Answer 1

a)

expected number of respondents without opinion =np=30*(1-0.32-0.58)=3

b)\

standard deviation of the number of respondents saying the country is going to the right direction =sqrt(np(1-p))

=sqrt(70*0.32*0.68)=3.9028

c)

probability that, of 8 voters, at least 5 of them say the country is on the wrong track. =P(X>=5)

==0.5473

d)

probability that any of those 8 respondents has/have no opinion. =1-(0.9)⁸ =0.5695

e)

here mean of distribution=μ=np=		3
and standard deviation σ=sqrt(np(1-p))=		1.6432

minimum usual value =μ-2*σ =		-0.29~0.00
maximum usual value =μ-2*σ =		6.29 ~6

“usual” interval for the number of responding without opinion ~ 0 to 6