Question

The Pew Research Center found that 38.6% of adult Americans believe that marriage is now obsolete. Suppose a random sample of 550 American adults is asked whether marriage is obsolete. Describe the sampling distribution of " role="presentation">pˆ by using the " role="presentation">N(mean,sd) notation and reporting the mean and standard deviation of the sample proportion of American adults who believe that marriage is now obsolete. What is the probability that in a random sample of 550 American adults that less than 35% believe that marriage is obsolete? Explain your method and TI calculation. What is the probability that in a random sample of 550 American adults that between 45% and 50% believe that marriage is obsolete? Explain your method and TI calculation. Would it be unusual for a random sample of 550 American adults to result in 260 or more who believe marriage is obsolete? How would you determine this?

Answer 1

ndutt T Pposton o ari cans belioe tot mmda now obsote () 0.386 (38.6%) Random ampla o Amarican adults ()550 Sampling distibution ot CSampla rposen) K unoer ob adut Ama can who belieuremat Me an )np 50X 0.386 212.3 1o atnd ho Ssoxo386x0-614 So of p七allows ormal diutian' The Samping distbukem ) (Ro mal ap proni maon to Binomid dintb with o.386 Angan 6.386x044 Oo208 Standard dariaton 2-ScRse -0.346 6.025 6 T robabii ttat in a Yandom Samde 6 5So Amadcan adults that es tzan 3 , bellaive That Maniag iA obaobte PL o.35) Pl2<-73) o.0418 Fist we tind t 2-Score 2 O.35-o386 O.0208 24-1-73 tables 6t the araa To tind Poloao it 8tandard nosmel distbtion we have te vse ia 2ェー1-73 Cumulative area ot The pookoali tis e auAwex Amarican i) The prebbk t sandom Sanple ot Sso in a adults TL betwean HS%. and 0' beiere that marriape s P(3.082 5.48)-0.00O Pos pso obsaate Clasakows: Scs 2,Ou O.386 O.D208 3.08 o 3 5.48 N2 30g J To tind tha raqired Pocal Standard noal areatele pobb Cuw atre areRa uptou edmals Godnad) wa have to e (Cumulave arta os) &) otZ.u 2 3.08 4. DO0O9990 o.0010

Sample ot 550 AnaiCon adults to resutin 210 o wore yandom a bei ve mar iage iA Sosoute ニplx>260) p(Z>1)くo0000) 2-Sore 260-212.3 11-4172 The probei iot adulto to yesult in 260 Sampe bdeive moriae i SSO Aesi on Tandom obs0ate io ver very ow Ciej o0)) So treatad a unsnal event es event
This problem is related to the Normal approximation to the Binomial distribution.