Question

It is estimated that 25% of households own a riding lawn mower. A sample of 16 households is studied. What is the probability that exactly 5 of these own a riding lawn mower?

Answer 1

From the data provided:
p = 25% = 0.25
1-p = 1-0.25 = 0.75
Sample size, n = 16
(n-k) = 16-5 = 11
k = 5

Probability that exactly 5 selected from the sample have lawn mower:
p(k=5) = (n,k)*p^k*(1-p)^(n-k) = [n!/(k)!(n-k)!]*p^k*(1-p)^(n-k) = [16!/(5)!(16-5)!]*0.25^5*(1-0.25)^(16-5) = 4368*(1/1024)*0.04224 = 0.1802

Therefore, probability that selected 5 households have a lawn mower is 0.1802 = 18.02%.