According to a survey in a country 33 of adults do not have

According to a survey in a country, 33% of adults do not have any credit cards. Suppose a simple random sample of 200 adults is obtained. Describe the sampling distribution of p, the sample proportion of adults who do not have a credit card. Choose the phrase that best describes the shape of the sampling distribution of p below. Approximately normal because n LE 0.05N and np(1-p) GE 10. Approximately normal because n LE 0.05N and np(1 -p)

Solution

here n=200, p=0.33
ANSWER OF PART (a) is A i.e. approximately normal becacuse n<=0.05N and np(1-p)>=10
here n=200, p(estimate)=0.33,q(estimate)= 1-p=0.67
mean of sampling distribution of p (estimate) is=n*p=200*0.33=66
Variarice of sampling distribution of p (estimate)=sqn*p*q=200*0.33*0.67=44.22
Standard deviation of sampling disribution p=square root of variance=square root(44.22)=6.65
ANSWER OF PART (b)
probability of less than 30% have no cards is
P(p<0.3)=1-P(Z=9.09)=1-0.1611=0.8389
ANSWER OF PART (C)