00:01
In this scenario, x represents the number of people who prefer the democratic candidate out of a random sample of 43 people.
00:07
Since each person's preference is independent and there are only two possible outcomes, prefer democratic or not, the distribution of x is a binomial distribution.
00:17
Given that 52 % of all voters prefer the democratic candidate, we can say that p is 0 .52.
00:23
That's the probability of success and the number of trials is 43.
00:27
I'm going to show you how to do this with the desmos graphing calculator.
00:30
If you go to functions and scroll down to distributions and pick the binomial distribution and ask for trials and success probability, well, this would be 43 trials with a probability of success of 0 .52 for 52%.
00:43
Then you click the cdf and you can start to answer your questions.
00:47
The probability of exactly 13 would be a minimum and a maximum of 13, so that's 0 .0020.
00:54
The formula for this by hand is 43 choose 13 times the probability of success 13 times, and then the probability of failure, which would be 48%, 30 times, because the exponents would have to total to the number of trials and you get the same value here...