00:01
This problem says 68 % of all americans live in cities with population greater than 100 ,000 people.
00:06
If 46 americans are randomly selected, find the probability that exactly 29 of them live in cities with population greater than 100 ,000, at most 31 for b, at least 29 for c, and then between 25 and 30, including 25 and 30, for our final probability.
00:22
And to figure this out, we are going to treat this as a binomial distribution because we have a success or failure probability.
00:29
Either we are going to have the population greater than 100 ,000 or we're not.
00:34
And we also have variables that are independent and that the probability that one city randomly selected having a population greater than 100 ,000, it's not going to affect the probability for the next city.
00:42
So for a, we want the probability of a specific event.
00:46
So we're going to use binomial pdf in our calculator since it's a specific event.
00:50
And we start off with our n value and p value, which is our 46 cities randomly selected for our number of trials, and the p value of 0 .68 that came from our 68%.
01:01
And that follows by the x value that we're trying to observe for the binomial pdf, which is 29 here.
01:07
And when we evaluate and round to four decimal places, we get the result of 0 .0940 for our first probability.
01:15
And then for the rest of our probabilities, we're still going to use binomial, but we're going to use binomial cdf because we are looking for the probability of a cumulative scenario.
01:23
And for our example for b, we want the probability that at most 31 have at least the or have greater than 100 ,000 population.
01:31
So that means we want 31 and everything less than that.
01:35
And for binomial cdf, we still start off with our number of trials, and then our p value...