One in five people in the United States own individual stocks. In a random sample of 12 people, what is theprobability that the number owning individual stocks is at least fourA 0.795B. 0.133C. 0.927D. 0.205

Answer:The correct option is D) 0.205.Step-by-step explanation:Consider the provided information.One in five people in the United States own individual stocks.That means [tex]p=\frac{1}{5}=0.2[/tex][tex]q=1-p=1-0.2=0.8[/tex]We need to find the probability that the number owning individual stocks is at least four.Let x represents the number of people own stocks.[tex]P(x\geq 4)=1-P(x=0)-P(x=1)-P(x=2)-P(x=3)[/tex][tex]P(x\geq 4)=1-^{12}C_0(0.2)^0(0.8)^{12}-^{12}C_1(0.2)^1(0.8)^{11}-^{12}C_2(0.2)^2(0.8)^{10}-^{12}C_3(0.2)^3(0.8)^{9}[/tex][tex]P(x\geq4 )=1-0.8^{12}-12\cdot0.2\cdot0.8^{11}-\frac{12!}{10!2!}0.2^{2}\cdot0.8^{10}-\frac{12!}{9!3!}0.2^{3}\cdot0.8^{9}[/tex][tex]P(x\geq4 )=1-0.79456[/tex][tex]P(x\geq4 )=0.20543[/tex]Hence, the correct option is D) 0.205.