Forty-nine percent of US teens have heard of a fax machine, then the probability that the teen has heard of a tax machine is p=0.49 and the probability that the tenn hasn't heard of a tax machine is q=1-p=1-0.49=0.51.
Use binomial distribution.
The probability that among 12 randomly selected teens exactly 6 have heard of a fax machine is
[tex]Pr(X=6)=C_{12}^6p^6q^{12-6}=\dfrac{12!}{6!(12-6)!}(0.49)^6(0.51)^6=\\\\\dfrac{6!\cdot 7\cdot 8\cdot 9\cdot 10\cdot 11\cdot 12}{6!\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6}(0.49\cdot 0.51)^6=924\cdot (0.2499)^6\approx 0.22505.[/tex]
The probability that among 12 randomly selected teens more than 8 have heard of a fax machine is
[tex]Pr(X>8)=C_{12}^9p^9q^{12-9}+C_{12}^{10}p^{10}q^{12-10}+C_{12}^{11}p^{11}q^{12-11}+C_{12}^{12}p^{12}q^{12-12}=\\\\\dfrac{12!}{9!(12-9)!}(0.49)^9(0.51)^3+\dfrac{12!}{10!(12-10)!}(0.49)^{10}(0.51)^2+\dfrac{12!}{11!(12-11)!}(0.49)^{11}(0.51)^1+\dfrac{12!}{12!(12-12)!}(0.49)^{12}(0.51)^0=220\cdot (0.49)^9(0.51)^3+66\cdot (0.49)^{10}(0.51)^2+12(0.49)^{11}(0.51)^1+(0.49)^{12}\approx 0.0638.[/tex]
