According to a survey in a​ country, 23​% of adults do not own a credit card. Suppose a simple random sample of 800 adults is obtained. Complete parts​ (a) through​ (d) below.   Click here to view the standard normal distribution table (page 1). LOADING... Click here to view the standard normal distribution table (page 2). LOADING... ​(a) Describe the sampling distribution of p​, 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 p below.     A. Not normal because n≤0.05N and np(1−p)≥10   B. Approximately normal because n≤0.05N and np(1−p)<10   C. Approximately normal because n≤0.05N and np(1−p)≥10   D. Not normal because n≤0.05N and np(1−p)<10 Determine the mean of the sampling distribution of p.   μp=nothing ​(Round to two decimal places as​ needed.) Determine the standard deviation of the sampling distribution of p.

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According to a survey in a​ country,
23​%
of adults do not own a credit card. Suppose a simple random sample of
800
adults is obtained. Complete parts​ (a) through​ (d) below.
 
Click here to view the standard normal distribution table (page 1).
LOADING...
Click here to view the standard normal distribution table (page 2).
LOADING...
​(a) Describe the sampling distribution of
p​,
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
p
below.
 
 
A.
Not normal because
n≤0.05N
and np(1−p)≥10
 
B.
Approximately normal because
n≤0.05N
and np(1−p)<10
 
C.
Approximately normal because
n≤0.05N
and np(1−p)≥10
 
D.
Not normal because
n≤0.05N
and np(1−p)<10
Determine the mean of the sampling distribution of
p.
 
μp=nothing
​(Round to two decimal places as​ needed.)
Determine the standard deviation of the sampling distribution of
p.
 
σp=nothing
​(Round to three decimal places as​ needed.)
​(b) What is the probability that in a random sample of
800
​adults, more than
24​%
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
800
adults were​ obtained, one would expect
nothing
to result in more than
24​%
not owning a credit card.
​(Round to the nearest integer as​ needed.)
​(c) What is the probability that in a random sample of
800
​adults, between
19​%
and
24​%
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
800
adults were​ obtained, one would expect
nothing
to result in between
19​%
and
24​%
not owning a credit card.
​(Round to the nearest integer as​ needed.)
​(d) Would it be unusual for a random sample of
800
adults to result in
152
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
p
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
p
is less than or equal to the sample proportion is
nothing​,
which is
less
than​ 5%.
 
C.
The result
is not
unusual because the probability that
p
is less than or equal to the sample proportion is
nothing​,
which is
greater
than​ 5%.
 
D.
The result
is
unusual because the probability that
p
is less than or equal to the sample proportion is
nothing​,
which is
greater
than​ 5%.
 
 
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