Question

10.5% 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 older.The probability that at most 2 are 65 or older is(Round to three decimal places as needed)

Answer 1

Given:

The sample size n=25

Probability of population is 65 or older is 10.5%.

This date follows the binomial distribution,

$\begin{gathered} n=25,p=0.105 \\ X\rightarrow B(n=25,p=0.105) \end{gathered}$

To find the probability that at most 2 are 65 or older,

$\begin{gathered} P(X=x)=^nC_x(p)^x(1-p)^{n-x} \\ P(0\leq X\leq2)=P(X=0)+P(X=1)+P(X=2) \\ =^{25}C_0(0.105)^0(1-0.105)^{25-0}+^{25}C_1(0.105)^1(1-0.105)^{25-1}+^{25}C_2(0.105)^2(1-0.105)^{25-2} \\ =0.0625+0.1832+0.2579 \\ =0.5036 \\ \approx0.504 \end{gathered}$

Answer: Probability is 0.504 .