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?

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%.