00:01
It's given here that 18 % of all americans live in poverty.
00:05
So that means for any randomly selected individual american, this probability is 0 .18.
00:11
And we consider a random selection of 34 americans.
00:15
And we're asked for the probabilities that certain numbers of these 34 live in poverty.
00:20
So let's define a random variable x as the number of americans in the sample of 34 that are living in poverty.
00:27
Here each of these 34 americans can be viewed as a bernoulli trial.
00:33
There's two outcomes of interest that either live in poverty or not.
00:37
And since it's a random sample, their outcomes are independent.
00:41
The number of americans living in poverty out of a given number of independent bernoulli trials is a binomial random variable.
00:52
So here x is a binomial, and the probability mass function for the binomial random variable is given by this formula.
01:10
And so for part a, we want the probability that exactly 7 of these 34 live in poverty.
01:16
This is the probability that x is equal to 7, using the probability mass function that's 34 to 7 times 0 .18 to the exponent 7, times 0 .82 to the exponent 27.
01:36
And this comes out to 0 .151 approximately.
01:40
For question b, we want the probability that at most 6 live in poverty.
01:48
This is the probability that x is less than equal to 6.
01:53
So let's use excel to solve this cumulative probability.
01:57
If we go to excel, we start a computation with an equal sign...