During the last student elections at a certain college 45 of

During the last student elections at a certain college, 45% of the students voted for the democratic student party. A simple random sample of students from this college is to be selected.

(a) If 12 students are to be selected, what is the distribution of the number of students in the sample who voted for the democratic student party?

(b) If 12 students are to be selected, what is the probability that more than 7 students in the sample voted for the democratic student party?

(c) If120studentsaretobeselected,whatisthe(approximate)distributionofthenumber of students in the sample who voted for the democratic student party?

Solution

a) according to the qustion it will be a binomial distribution with probability = 0.45 and the value will go from 1 to 12

hence the distribution is
Binomial distribution with n=12, p=.45 , x=0,1,2,....,12

b)
P( x =k) = 12Ck (.45)^k (.55)^(12-k)

k is the the number for which we are finding the probability
in this we have to add the probability with x =7 and more till 12
x p(x)
7 0.148945
8 0.076165
9 0.027696
10 0.006798
11 0.001011
12 0.000069

Add: P( x >=7 ) = 0.260685

c)
as the sample size is large, the probability distribution is normal with mean np =120(.45) =54 and variance np(1-p) = 120(.45)(.55) = 29.7