00:01
So this problem tells us that in the u .s.
00:04
71 .2 % of college students agreed, yes, that they believe same -sex couples should have the right to legal marital status.
00:13
It says that we randomly pick six of these students from the survey, and we're interested in the number that believe that same -sex couples should have the right to legal marital status.
00:22
It asks us to find the probability that at least two of these students say yes.
00:26
So first of all here, we need to recognize that what we're dealing is a binomial, dealing with is a binomial distribution problem.
00:36
And it's a binomial distribution because in the survey there's only two possible outcomes.
00:41
One is yes, i believe that same sex couples should be able to legally bury.
00:47
And the second option is no, they believe that they should not be allowed to legally marry.
00:51
Since we have only two possible options here, we're dealing with a binomial experiment, which means we need to first define our variables.
00:57
Variables, which are n, p, and q.
01:01
N is the number of the sample, the number in the sample.
01:05
It says that we pick six students, so n is equal to six.
01:09
P is the probability of success, or in this case the probability that they say yes, and we're told that is 71 .2%.
01:18
As a decimal, that would be .712, and then q is always 1 minus p, or the probability of failure, so 1 minus 0 .712 gives us 0 .288.
01:35
Now, now that we have our variables, we need to find the mean and standard deviation because we'll need that for our problem.
01:42
The mean and standard deviation equations for binomial distribution are on the screen here in red.
01:47
So we'll start with the mean.
01:49
The mean you can see is equal to n times p.
01:51
Our n is 6, and our p is 0 .712.
01:55
When we multiply those together, we get 4 .272 as our mean...