It is estimated that 30% of households own a riding lawn mower. A sample of 10 households is studied. What is the probability that more than 7 of these own a riding
Lawn mower?
A) 0.0016
B) 0.9894
C) 0.0001
D) 0.0106

Question

Quizplus · Accepted Answer

The probability of a household owning a riding lawn mower is 0.3. The probability of a household not owning a riding lawn mower is 0.7. The probability of more than 7 households owning a riding lawn mower is the complement of the probability of 7 or fewer households owning a riding lawn mower. The probability of 7 or fewer households owning a riding lawn mower is the sum of the probabilities of 0, 1, 2, 3, 4, 5, 6, or 7 households owning a riding lawn mower. The probability of 0 households owning a riding lawn mower is 0.7^10 = 0.0282. The probability of 1 household owning a riding lawn mower is 10 * 0.3 * 0.7^9 = 0.1974. The probability of 2 households owning a riding lawn mower is 45 * 0.3^2 * 0.7^8 = 0.3948. The probability of 3 households owning a riding lawn mower is 120 * 0.3^3 * 0.7^7 = 0.4935. The probability of 4 households owning a riding lawn mower is 210 * 0.3^4 * 0.7^6 = 0.4284. The probability of 5 households owning a riding lawn mower is 252 * 0.3^5 * 0.7^5 = 0.2916. The probability of 6 households owning a riding lawn mower is 210 * 0.3^6 * 0.7^4 = 0.1544. The probability of 7 households owning a riding lawn mower is 120 * 0.3^7 * 0.7^3 = 0.0666. The sum of these probabilities is 0.0282 + 0.1974 + 0.3948 + 0.4935 + 0.4284 + 0.2916 + 0.1544 + 0.0666 = 0.9894. The complement of this probability is 1 - 0.9894 = 0.0016.

It Is Estimated That 30% of Households Own a Riding