According to a recent united states census bureau report 132...

According to a recent United States Census Bureau report, 13.2% of the population live below the poverty level. You plan to randomly sample 25 Americans. 1. What is the probability that your sample will include at least two people with incomes below the poverty level? 2. What is the expected value of the number of people in your sample with incomes below the poverty level? What is the standard deviation?

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00:01 Hi, i'm david and i'm here to help you answer your question.

00:04 Now let me bring up your question here.

00:06 In the question here, we're going to review about the binomial distribution.

00:10 Let me remind you that if we have the x that followed by the binomial with the n and the p, and then the problem predict of the x equal to k, equal to n choose k, p power k times 1 minus p, power n minus k.

00:27 Also exported under x equal to n times b.

00:31 And the variance of the x, standard division of the x, equal to the square root of the n times b times 1 minus b.

00:41 Now in this question here we have the 13 .2 % of the population leave below the power 3 level.

00:48 So it means that will be equal to the 0 .132.

00:52 We have the sum of n equal to the 25 americans.

00:56 So if we define x equal to the number of the americans.

01:03 That leave below the poverty level.

01:17 So therefore x is followed by the binomial and equal to the 25 p equals 1, 3 ,2.

01:26 Now for the question 1, i'm going to find the probability that it will include unless 2 people, so x will be greater equal to 2.

01:36 So to find this probability, we can take the comment 1 minus probability that x equals 0 and x can take the value of the 1.

01:45 Now we can use the formula for the binomial.

01:49 So we have the first 1 x into 0 and 25 to 0 0...

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