Question

According to a survey in a​ country, 22​% of adults do not own a credit card. Suppose a simple random sample of 200 adults is obtained. Complete parts​ (a) through​ (d) below. ​(a) Describe the sampling distribution of ModifyingAbove p with caret​, the sample proportion of adults who do not own a credit card. Choose the phrase that best describes the shape of the sampling distribution of ModifyingAbove p with caret below. A. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10 B. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10 C. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10 D. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10 Determine the mean of the sampling distribution of ModifyingAbove p with caret. mu Subscript ModifyingAbove p with caret Baseline equals nothing ​(Round to two decimal places as​ needed.) Determine the standard deviation of the sampling distribution of ModifyingAbove p with caret. sigma Subscript ModifyingAbove p with caretequals nothing ​(Round to three decimal places as​ needed.) ​(b) What is the probability that in a random sample of 200 ​adults, more than 25​% do not own a credit​ card? The probability is nothing. ​(Round to four decimal places as​ needed.) Interpret this probability. If 100 different random samples of 200 adults were​ obtained, one would expect nothing to result in more than 25​% not owning a credit card. ​(Round to the nearest integer as​ needed.) ​(c) What is the probability that in a random sample of 200 ​adults, between 20​% and 25​% do not own a credit​ card? The probability is nothing. ​(Round to four decimal places as​ needed.) Interpret this probability. If 100 different random samples of 200 adults were​ obtained, one would expect nothing to result in between 20​% and 25​% not owning a credit card. ​(Round to the nearest integer as​ needed.) ​(d) Would it be unusual for a random sample of 200 adults to result in 40 or fewer who do not own a credit​ card? Why? Select the correct choice below and fill in the answer box to complete your choice. ​(Round to four decimal places as​ needed.) A. The result is unusual because the probability that ModifyingAbove p with caret is less than or equal to the sample proportion is nothing​, which is less than​ 5%. B. The result is not unusual because the probability that ModifyingAbove p with caret is less than or equal to the sample proportion is nothing​, which is less than​ 5%. C. The result is unusual because the probability that ModifyingAbove p with caret is less than or equal to the sample proportion is nothing​, which is greater than​ 5%. D. The result is not unusual because the probability that ModifyingAbove p with caret is less than or equal to the sample proportion is nothing​, which is greater than​ 5%.

Answer 1

C. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10

mean of the sampling distribution =0.22

std error of proportion=σp=√(p*(1-p)/n)=

0.029

b)

probability =

P(X>0.25)

=

P(Z>1.03)=

1-P(Z<1.03)=

1-0.8485=

0.1515

. If 100 different random samples of 200 adults were​ obtained, one would expect 15 to result in more than 25​% not owning a credit card.

c)

probability =

P(0.2<X<0.25)

=

P(-0.69<Z<1.03)=

0.8485-0.2451=

0.6034

If 100 different random samples of 200 adults were​ obtained, one would expect 60  to result in between 20​% and 25​% not owning a credit card

d)

  D. The result is not unusual because the probability that ModifyingAbove p with caret is less than or equal to the  sample proportion is 0.2451 , which is greater than​ 5%.