A recent study shows that 35% of adult Americans believe that marriage is obsole

Question

A recent study shows that 35% of adult Americans believe that marriage is obsolete.

A) Suppose a random sample of 200 adult Americans is asked whether marriage is obsolete. Find the mean of the sampling distribution and the standard deviation

Mean= Standard deviation=

B) in a random sample of 200 adult Americans what is the probability that less than 33% believe that marriage is obsolete.

C) would it be unusual for a sample 200 adult Americans to result 84 or more who believe that marriage is obsolete?

Explanation / Answer

SolutionA:

np=200(0.35)=70

np(1-p)=200(0.35)(1-0.35)=45.5>10

p^=sample proportion follows normal distribution

mean=p^=0.35

stddeviation=sqr[t(0.35)(1-0.35)/200]

=0.0337

solutionB:

P(p^<0.33)

z=p^-p0/sqrt[p0(1-p0)/n]

=0.33-0.35/sqrt[0.35(1-0.35)/2]

z =-0.02/0.0337

z =-0.593

P(Z<-0.593)

P ( Z<0.593 )=1P ( Z<0.593 )=10.7224=0.2776

ANSWER :0.2776

sOLUTIONC:

p^=x/n=84/200=0.42

P(p^>0.42)

=0.42-0.35/sqrt[0.35(1-0.35)/200]

=0.07/0.0337

z =2.075

P(z>2.075)

P ( Z>2.075 )=1P ( Z<2.075 )=10.9812=0.0188

YES THIS IS UNUSUAL

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