Question

It is estimated that 35% of households own a riding lawn mower. A sample 19 households is studied. What is the mean number of households who own a riding lawn mower

Answer 1

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:

$E(X) = np$

35% of households own a riding lawn mower.

This means that $p = 0.35$

A sample 19 households is studied.

This means that $n = 19$

What is the mean number of households who own a riding lawn mower

$E(X) = np = 19*0.35 = 6.65$

The mean number of households who own a riding lawn mower is 6.65.