00:01
So we are told that according to a recent census, about 65 % of all households in the united states are made up of one or two people.
00:09
And we're going to assume this percentage is still valid.
00:12
And so this is a proportion, 0 .65.
00:14
And we want to know the probability that in a sample of 100 randomly selected households, that between 590 and 625 households are made up of one or two people.
00:39
So essentially we want to know the probability that exists between this.
00:41
And we're doing inclusive.
00:44
And so because we're given a proportion, we might want to think we're going to do a proportion test, but we're not.
00:50
We're actually going to do a test using a binomial, a normal approximation to the binomial.
00:56
Because we have this fixed probability, this fixed number of trials.
01:00
And so distribution, here's our normal distribution, which we're going to approximate our binomial with.
01:09
Oh my gosh, let's get that, maybe that's a little bit better.
01:13
There's our normal distribution.
01:15
Let me try one more time.
01:19
Fourth time's the charm, there we go.
01:20
Alright, that's okay.
01:22
And here's the mean, which is not going to be 0 .6.
01:25
The mean is actually going to be n times p, so it's going to be 650.
01:31
Because in a binomial distribution, the mean is n times p.
01:35
And we're going to call the variable x, our binomial random variable, where x is the number of households made up of one or two people.
01:43
And so we want to be between 590 and 625, which is roughly here.
01:46
So here's 590, here's roughly 625.
01:50
And we want to find the probability being between those.
01:53
Now something to note is our normal distribution is continuous, but our binomial is discrete.
01:58
Because we're going to consider this a binomial, which is discrete.
02:03
And to do this, we actually need to make sure we include 590 and include 625.
02:08
We need to go a little bit below 590 and a little bit above 625.
02:14
And that's called the continuity correction.
02:23
And what we do is we just add or subtract a half.
02:27
And that ensures that we capture that value.
02:32
So essentially what we're going to do is we're going to modify this...