Question

11.9% of the population is 65 or older. Find the probability that the following number of persons selected at random from 25 people are 65 or olderThe probability that at most 2 are 65 or older is(Round to three decimal places as needed)

Answer 1

11.9% of a population is 65 or older.

That is;

`\begin{gathered} P(65\text{ or older) = 0.119} \\ P(\text{younger than 65) = 0.881} \end{gathered}`

The probability of at most 2 is;

`\begin{gathered} P(at\text{ most 2)=P(none) + P( one is older) + (two are older)} \\ P(none)=^(25)C_0(0.119)^0(0.881)^(25) \\ P(none)=1(1)(0.0421) \\ P(none)=0.0421 \end{gathered}`
`\begin{gathered} P(1)=^(25)C_1(0.119)^1(0.881)^(24) \\ P(1)=25(0.119)(0.0478) \\ P(1)=0.1422 \\ P(2)=^(25)C_2(0.119)^2(0.881)^(23) \\ P(2)=300(0.119)^2(0.881)^(23) \\ P(2)=0.2305 \end{gathered}`
`\begin{gathered} P(at\text{ most 2)=0.0421+0.1422+0.2305} \\ P(at\text{ most 2)=}0.4148 \end{gathered}`

The probability that at most 2 are 65 or older is 0.415 (round to three decimal places)