Question

need help with 11,12, and 13

8. Ir 200 people are randomly selected, what is the probability that more than 25% of them voted in the primary? 0.20 0.20x0.80 -0.0283 -P(p<.05). 200 = 0.0386 9. In the state of North Carolina, there are 6,674.209 registered voters. In the May 2018 Primary election, 957,627 people voted. What is the population proportion of voters? (Round to the nearest percent) population proportion = 957627/6,674,209 0.14 10. If a random sample of 30 people from North Carolina is taken, what is the probability that 16% of them voted? P(V=0.16x30=48) = P148445) = P14/50 <P<5/30) P 10.1333<< 0.1647 (0,4196) + 10:10571-4 = 0.2047 11. If a random sample of 100 people from North Carolina is taken, what is the probability that more than 25% of them voted? 12. If a random sample of 100 people from North Carolina is taken, what is the probability that the proportion of people in the sample who voted differs from the population proportion by more than 2%? 13. If a random sample of 100 people from North Carolina is taken, what is the probability that the proportion of people in the sample who voted differs from the population proportion by less than 1%?

Answer 1

1 PC > 0.25) = |- PC & € 0.25) = -Pli- 0.14 0.25-0014 (0.148(1-0:14) - 100 1001484 0:14) 100 el- & ( 311701) 21-059992 = 0.0008 (1.1 Ams)

12) FF F-0. It )>0.02 = p [ Locompagnons gi02 Or 14 X (10.14) 0.148 (1-0.14) 100 0.02 0.14 X (1-0014) foo F . = 1-8 (0.5764) = 1-0. 717 8 = 0.2822 (12 Aus)

- 0.14 20.01 0.14 *(1-0119) 0.14 X1140119) 100 12 (0.2882) = 0.6134 (3 An)

Notesta) If we take P[1P - 0.14170.02] then ar aus becomes 2x0.28 82=0.5644

Note : - (13) If we take Prip- 0.141 20.01] then our answer beames 2x10.6134) - 1 =o" 2268

o As - 0.14 0.14 X 11-0.14) a N(0,1) V 100

because as per CLT, for large value of n,

Maps OPCI- Vn where p is population I proportion

Here n is 100,very large, so applied CLT.

Here, p=0.14,found out in part 9.

If there is any understanding problem regarding this please feel free to ask any doubt in comment box. THANK YOU.