Answer:
The mean number of households who own a riding lawn mower is 6.65.
Step-by-step explanation:
For each household, there are only two possible outcomes. Either there is a riding lawn mower, or there is not. The probability of a household having a riding lawn mower is independent of other households. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
35% of households own a riding lawn mower.
This means that [tex]p = 0.35[/tex]
A sample 19 households is studied.
This means that [tex]n = 19[/tex]
What is the mean number of households who own a riding lawn mower
[tex]E(X) = np = 19*0.35 = 6.65[/tex]
The mean number of households who own a riding lawn mower is 6.65.
