00:01
This problem says that it's claimed that 71 % of all americans live in cities with population greater than 100 ,000 people.
00:06
Based on this, if 42 americans are randomly selected, find the probability that x is equal to 28, and then x is at most 30 or less than or equal to 30, at least 29 or greater than or equal to 29, and then between 29 and 34 with those values inclusive.
00:21
And then lastly, we want to know the mean and the standard deviation of the distribution.
00:25
And the way we're going to find these probabilities is by treating this as a binomial distribution where we have a probability that's considered success or failure.
00:32
Either we are going to live in a city with a population greater than 100 ,000 or we're not.
00:36
And we also have events that are independent from each other, and that the probability of one american living in a 100 ,000 population city or not doesn't affect the probability for the next american.
00:46
So for binomial pdf, we use that when we want a specific probability, and that's the case for a, where we want the probability of exactly 28 live in a 100 ,000 city.
00:56
And for binomial pdf we started off with the n -value and p -value of the distribution and here we had 42 for the n -value with the probability of success of 0 .71 from 71 percent and then we list the x value we're looking to observe in this case 28 and when we evaluate there and round to four decimal places we'll get our probability and when we round to four decimal places we get the result of 0 .1076 and for our next probabilities, we're going to use binomial cdf because we want cumulative probabilities with either less than, greater than, or between values.
01:30
And for b, we want the probability that we're less than or equal to 30.
01:33
So for binomial cdf, we also start with the n -value and p -value of 42 and 0 .71...