107 of the population is 65 or older Find the probability th

10.7% 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 exactly 5 are 65 or older is

Solution

p = 10.7% = 0.107

q = 1- 0.107 = 0.893

Binomial probability distribution: nCr(p)^r(q^(n-r) )

n = 25 ; r =5

Probability of exactly 5 people older than 65 or older = 25C5(0.107)^5(0.893)^20

= 0.078