00:01
Given in this question that the rate of us home ownership was 65 .9%.
00:08
So that means for any randomly selected individual homeowner, the probability of owning their home is .659.
00:16
We consider a random sample of 120 households across the us, and we were asked for the probability that 65 to 85 inclusive of these 120 live in homes that they own.
00:30
So let's first define a random variable x as the number of people in the sample of 120 who live in houses that they actually own.
00:43
In this scenario, the 120 randomly sampled households can be thought of as for newly trials having two outcomes of interest.
00:52
The people who live in them either own them or not.
00:56
And since it's a random sample, their outcomes are independent.
00:59
And so the number of successes in a fixed number of independent for newly trials is a binomial random variable.
01:07
So here, x is a binomial random variable based on 120 trials and probability of success .659.
01:17
We want to find the probability that x is between 65 and 85 inclusive...