Question

One in five people in the United States own individual stocks. In a random sample of 12 people, what is the

probability that the number owning individual stocks is at least four

A 0.795

B. 0.133

C. 0.927

D. 0.205

Answer 1

The correct option is D) 0.205.

Explanation:

Consider the provided information.

One in five people in the United States own individual stocks.

That means
`p=(1)/(5)=0.2`

`q=1-p=1-0.2=0.8`

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.

`P(x\geq 4)=1-P(x=0)-P(x=1)-P(x=2)-P(x=3)`

`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)`

`P(x\geq4 )=1-0.8^(12)-12\cdot0.2\cdot0.8^(11)-(12!)/(10!2!)0.2^(2)\cdot0.8^(10)-(12!)/(9!3!)0.2^(3)\cdot0.8^(9)`

`P(x\geq4 )=1-0.79456`

`P(x\geq4 )=0.20543`

Hence, the correct option is D) 0.205.