A recent study shows that 35% of adult Americans believe that marriage is obsole
ID: 3240756 • Letter: A
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A recent study shows that 35% of adult Americans believe that marriage is obsolete.
A) Suppose a random sample of 200 adult Americans is asked whether marriage is obsolete.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B) in a random sample of 200 adult Americans what is the probability that less than 33% believe that marriage is obsolete.
C) would it be unusual for a sample 200 adult Americans to result 84 or more who believe that marriage is obsolete?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