Question

According to a study conducted in one​ city,

3131​%

of adults in the city have credit card debts of more than​ $2000. A simple random sample of

n equals 300n=300

adults is obtained from the city. Describe the sampling distribution of

ModifyingAbove p with caretp​,

the sample proportion of adults who have credit card debts of more than​ $2000. Round to three decimal places when necessary.

A.Approximately​ normal;

mu Subscript pμpequals=0.310.31​,

sigma Subscript pσpequals=0.0270.027

B.Approximately​ normal;

mu Subscript pμpequals=0.310.31​,

sigma Subscript pσpequals=0.0010.001

C.Exactly​ normal;

mu Subscript pμpequals=0.310.31​,

sigma Subscript pσpequals=0.0270.027

D.​Binomial;

mu Subscript pμpequals=9393​,

sigma Subscript pσpequals=8.011

Answer 1

Solution

Given that,

p = 0.31

1 - p = 1 - 0.31 = 0.69

n = 300

= p = 0.31

=  [p ( 1 - p ) / n] = [(0.31 * 0.69) / 300 ] = 0.027

A) Approximately normal   = 0.31 and   = 0.027