1) A machine that fills milk cartons underfills a certain proportion p. If 50 ca

Question

1) A machine that fills milk cartons underfills a certain proportion p. If 50 cartons are randomly selected from the outlet of this machine, find the probability that no more then 2 cartons are underfilled when: (A) p=0.05. (B) p= 0.1. 2) During the 2002 Survey of Business Owners (SBO), it was found that the numbers of female-owned, male-owned, and jointly male-and female-owned businesses were 6.5, 13.2, and 2.7 million, respectively. among four randomly selected businesses, find the probabilities of the following events. (A) All four had a female but no male owner (B)One of the four was either owned or co-owned by a male (C) None of the four were jointly owned by a female and male

Explanation / Answer

1)p(at most 2 unfilled)=p(minimum 48 are filled)=p(exactly 48 filled)+p(exactly 49 filled)+p(exactly 50 filled)=0.05^(2)*(1-0.05)^48+0.05^(1)*(1-0.05)^49+(1-0.05)^50

when p=0.1 then 0.1^(2)*(1-0.1)^48+0.05^(1)*(1-0.1)^49+(1-0.1)^50

2)p(f owned)=6.5/(6.5+13.2+2.7)

p(m owned)=13.2/(6.5+13.2+2.7)

p(jointly hold)=2.7/(6.5+13.2+2.7)

a)p(f)^4

c)(1-p(jointly hold))^4

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