Suppose that 40% of Iowans are in favor of a presidential candidate. A pollster

Question

Suppose that 40% of Iowans are in favor of a presidential candidate. A pollster selects a random sample of 10 Iowans and asks them about their opinions (in favor/not in favor) about the candidate. Let X be the number of people in the sample who are in favor of the candidate (a) What is the sample space of X? b) What is the distribution of X? (c) What is the probability that 5 people in the sample are in favor of the candidate? (d) What is the probability that 3 to 5 people in the sample are in favor of the candidate? e) What is the probability that at least 6 of the people in the sample are in favor of the candidate?

Explanation / Answer

Ans:

a)Sample space for X

S={0,1,2,3,......10}

b)Binomial distribution with n=10,p=0.4

P(x=r)=10Cr*pr*(1-p)10-r

c)P(x=5)=10C5*0.45*0.65=0.2007

d)P(x=3,4,5)=p(x=3)+p(x=4)+p(x=5)=0.2150+0.2508+0.2007=0.6665

e)P(x>=6)=p(x=6)+p(x=7)+p(x=8)+p(x=9)+p(x=10)

=0.1115+0.0425+0.0106+0.0016+0.0001=0.1663

x p(x) 0 0.0060 1 0.0403 2 0.1209 3 0.2150 4 0.2508 5 0.2007 6 0.1115 7 0.0425 8 0.0106 9 0.0016 10 0.0001

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