Question

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) 0.028
B) 0.038
C) 0.048
D) 0.058

Answer 1

The probability that more than 7 households own a riding lawn mower out of 10 households is approximately 0.1499.

Step-by-step explanation:

To find the probability that more than 7 of the 10 households own a riding lawn mower, we will use the binomial probability formula.

First, we need to calculate the probability that exactly 7 households own a riding lawn mower. This can be found using the binomial probability formula:

P(X = 7) = (10 choose 7) * (0.3)^7 * (0.7)^3 = 0.2668

Next, we need to calculate the probabilities for 8, 9, and 10 households owning a riding lawn mower:

P(X = 8) = (10 choose 8) * (0.3)^8 * (0.7)^2 = 0.1211

P(X = 9) = (10 choose 9) * (0.3)^9 * (0.7)^1 = 0.0282

P(X = 10) = (10 choose 10) * (0.3)^10 * (0.7)^0 = 0.0006

Finally, we can add up these probabilities to find the probability that more than 7 households own a riding lawn mower:

P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1211 + 0.0282 + 0.0006 = 0.1499

So, the probability that more than 7 of the 10 households own a riding lawn mower is approximately 0.1499, which is closest to option B) 0.038.