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

10.8% 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 none are 65 or older is.003.(Type an integer or decimal rounded to the nearest thousandth as needed.) The probability at least 3 are 65 or older is (Type an integer or decimal rounded to the nearest thousandth as needed.)

Solution

p = 10.8% = 0.108

q = 1-p = 0.892

selected 50 people = n

binomial distribution of probability : nCrp^r(q)^(n-r)

a) none : r=0 ; 50C0(0.892)^50 =0.003

b) At least 3 are older that 65: 1 - Probability(none +one person older than 65 + 2persons  older than 65)

= 1 - ( 0.003 + 50C1(0.108)(0.892)^49 + 50C2(0.108)^2(0.892)^48 )

= 1 - (0.003 + 0.020 + 0.059 )

= 0.918