Suppose a simple random sample of sizenequals=200is obtained from a population whose size isUpper N equals 30 comma 000N=30,000and whose population proportion with a specified characteristic isp equals 0.6 .p=0.6.Complete parts ​(a) through​ (c)below.​(a) Describe the sampling distribution ofModifyingAbove p with caretp.Choose the phrase that best describes the shape of the sampling distribution below.  A.Not normal becausen less than or equals 0.05 Upper Nn≤0.05Nand np left parenthesis 1 minus p right parenthesis greater than or equals 10.np(1−p)≥10. B.Not normal becausen less than or equals 0.05 Upper Nn≤0.05Nand np left parenthesis 1 minus p right parenthesis less than 10.np(1−p)<10. C.Approximately normal becausen less than or equals 0.05 Upper Nn≤0.05Nand np left parenthesis 1 minus p right parenthesis greater than or equals 10.np(1−p)≥10. D.Approximately normal becausen less than or equals 0.05 Upper Nn≤0.05Nand np left parenthesis 1 minus p right parenthesis less than 10.np(1−p)<10. Determine the mean of the sampling distribution ofModifyingAbove p with caretp. mu Subscript ModifyingAbove p with caret Baseline equalsμp=nothing​(Round to one decimal place as​ needed.)

Question
Asked Nov 17, 2019
Suppose a simple random sample of size
nequals=200
is obtained from a population whose size is
Upper N equals 30 comma 000N=30,000
and whose population proportion with a specified characteristic is
p equals 0.6 .p=0.6.
Complete parts ​(a) through​ (c)
below.
​(a) Describe the sampling distribution of
ModifyingAbove p with caretp.
Choose the phrase that best describes the shape of the sampling distribution below.
 
 
A.
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 10.np(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 less than 10.np(1−p)<10.
 
C.
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 10.np(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 less than 10.np(1−p)<10.
 
Determine the mean of the sampling distribution of
ModifyingAbove p with caretp.
 
mu Subscript ModifyingAbove p with caret Baseline equalsμp=nothing
​(Round to one decimal place as​ needed.)
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Expert Answer

Step 1

It is given that n is 200, N is 30,000 and p is 0.6.

Step 2

In general, the sampling distribution is approximately normal if n is less than or ...

0.05N 0.05(30,000)
1,500
np(1-p)- 200x 0.6(1-0.6)
=48
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0.05N 0.05(30,000) 1,500 np(1-p)- 200x 0.6(1-0.6) =48

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