According to a poll on consumer behavior, 36% of people say they will only consi

Question

According to a poll on consumer behavior, 36% of people say they will only consider cars manufactured in their country when purchasing a new car. Suppose you select a random sample of 100 respondents. Complete parts (a) through (c) below. a. What is the probability that the sample will have between 29% and 40% who say they will consider only cars manufactured by a company in their country when purchasing a new car? The probability is b. The probability is 80% that the sample will be contained within what symmetrical limits of the population percentage? The probability is 80% that the sample percentage will be contained above % and below % c. The probability is 99.7% that the sample will be contained within what symmetrical limits of the population percentage? The probability is 99.7% that the sample percentage will be contained above % and below %.

Explanation / Answer

A. Here p=0.36 and n=11

So as per sample proportion distribution

Mean=p=0.36 and sd=sqrt(p(1-p)/n)=0.048

P(0.29<p<0.40)=P(0.29-0.36/0.048<z<0.40-0.36/0.048)=P(-1.46<z<0.83)=P(0<z<0.83)-P(0<z<-1.46)= 0.2967-( -0.4279)= 0.7246

B. P(-p<phat<p)=0.80

P(-1.282<z<1.282)=0.80

z=p-mean/SE=-1.282

p=-1.282*0.048+0.36=0.298

Also z=p-mean/SE=1.282

p=1.282*0.048+0.36=0.42

c. P(-p<phat<p)=0.997

P(-2.968<z<2.968)=0.997

z=p-mean/SE=-2.968

p=-2.968*0.048+0.36=0.22

Also z=p-mean/SE=2.968

p=2.968*0.048+0.36=0.50

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