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

11.8% of the population is 65 or older. Find the probability that the following number of persons selected at random from 50 people are 65 or older. The probability that exactly 5 are 65 or older is

Solution

p = 11.8% = 0.118

q = 1- 0.118 = 0.882

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

n = 50 ; r =5

Probability of exactly 5 people older than 65 or older = 50C5(0.118)^5(0.882)^45

= 0.170