Chapter 6, Section 6.3, Question E28 According to a recent United States Census

Question

Chapter 6, Section 6.3, Question E28 According to a recent United States Census Bureau report, 13.2% of the population live below the poverty level. You plan to randomly sample 30 Americans a. What is the probability that your sample will include at least two people with incomes below the poverty level? Round the answer to 4 decimal places b. What are the expected value and standard deviation of the number of people in your sample with incomes below the poverty level? Expected value Standard deviation - Round the answer to 4 decimal places m your region. How many people in your c. You want to see if the percentage of 13.2% holds or the region in which you live. You take a random sa pe of a peo e ro sample would have to live below the poverty level before you have reason to believe that the percentage in your region is higher than 13.2%? people

Explanation / Answer

a)

p=0.132

q=1-p =1-0.132 =0.868

n=30

P=nCr p^r q^(n-r)

P(x>= 2) =P(x=2) +P(x>2)

               =P(x=2) + 1-P(x<= 2)

               =30C2 (0.132)^2 (0.868)^(28) + 1 - 0.223529106

               = 0.143942627 + 1 - 0.223529106

               = 0.9204

b)

Expected value = n*p = 30*0.132 = 3.96

standard deviation = sqrt(npq) =sqrt(30*0.132*0.868) =1.8540

c)

number of people = n*p =30*0.132 = 4

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