Question

According to a survey in a​ country, 27​% of adults do not own a credit card. Suppose a simple random sample of 500 adults is obtained. Complete parts​ (a) through​ (d) below.

​(a) Describe the sampling distribution of

ModifyingAbove p with caretp​,

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 caretp

below.

A.Approximately normal because

n less than or equals 0.05 Upper Nn≤0.05N

and np left parenthesis 1 minus p right parenthesis less than 10np(1−p)<10

B.Not normal because

n less than or equals 0.05 Upper Nn≤0.05N

and np left parenthesis 1 minus p right parenthesis greater than or equals 10np(1−p)≥10

C.Not normal because

n less than or equals 0.05 Upper Nn≤0.05N

and np left parenthesis 1 minus p right parenthesis less than 10np(1−p)<10

D.Approximately normal because

n less than or equals 0.05 Upper Nn≤0.05N

and np left parenthesis 1 minus p right parenthesis greater than or equals 10np(1−p)≥10Determine the mean of the sampling distribution of

ModifyingAbove p with caretp.

mu Subscript ModifyingAbove p with caret Baseline equalsμp=nothing

​(Round to two decimal places as​ needed.)Determine the standard deviation of the sampling distribution of

ModifyingAbove p with caretp.

sigma Subscript ModifyingAbove p with caretσpequals=nothing

​(Round to three decimal places as​ needed.)​(b) What is the probability that in a random sample of

500500

​adults, more than

2828​%

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

500500

adults were​ obtained, one would expect

nothing

to result in more than

2828​%

not owning a credit card.

​(Round to the nearest integer as​ needed.)

​(c) What is the probability that in a random sample of

500500

​adults, between

2323​%

and

2828​%

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

500500

adults were​ obtained, one would expect

nothing

to result in between

2323​%

and

2828​%

not owning a credit card.

​(Round to the nearest integer as​ needed.)

​(d) Would it be unusual for a random sample of

500500

adults to result in

115115

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

isis

unusual because the probability that

ModifyingAbove p with caretp

is less than or equal to the sample proportion is

nothing​,

which is

lessless

than​ 5%.

B.The result

isis

unusual because the probability that

ModifyingAbove p with caretp

is less than or equal to the sample proportion is

nothing​,

which is

greatergreater

than​ 5%.

C.The result

is notis not

unusual because the probability that

ModifyingAbove p with caretp

is less than or equal to the sample proportion is

nothing​,

which is

greatergreater

than​ 5%.

D.The result

is notis 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%.

Answer 1