Seventy per cent of the student body of a very large postsec

Seventy per cent of the student body of a very large post-secondary institution is female. In a random sample of 12 students, what is the probability that

a. at most half will be females?

b. more than 7 will be females?

c. fewer than 3 will be males?

Solution

70% OF THE STUDENT BODY OF A very large post secondary institution is female. in a random sample of 12 students what is the probability that
a)at most half will be females?
P(0<= x <=6) = 12C6(0.7)^6*(0.3)^6 = binompdf(12,0.7.6) = 0.0792
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b) more than 7 will be females?
P(7<= x <=12) = 1-answer to part a = 1-0.0792 = 0.9208

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c) fewer than 3 will be males
P(0<= x <=2) = 12C3(0.3)^3*(0.7)^9 = 0.1678