uppose a simple random sample of size n=125 is obtained from a population whose size is N=10,000 and whose population proportion with a specified characteristic is p=0.4. Complete parts ​(a) through​ (c) below. ​(a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution 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. Not normal because n≤0.05N and np(1−p)<10.   D. Approximately normal because n≤0.05N and np(1−p)≥10.   Determine the mean of the sampling distribution of p.   μp=nothing ​(Round to one decimal place as​ needed.)   Determine the standard deviation of the sampling distribution of p.   σp=nothing ​(Round to six decimal places as​ needed.)   ​(b) What is the probability of obtaining x=55 or more individuals with the​ characteristic? That​ is, what is ​P(p≥0.44​)?   ​P(p≥0.44​)=nothing ​(Round to four decimal places as​ needed.)   ​(c) What is the probability of obtaining x=40 or fewer individuals with the​ characteristic?   ​P(p≤0.32​)=nothing ​(Round to four decimal places as​ needed.)

 
Suppose a simple random sample of size

n=125

is obtained from a population whose size is

N=10,000

and whose population proportion with a specified characteristic is

p=0.4.

Complete parts ​(a) through​ (c)

below.
​(a) Describe the sampling distribution of

p.
Choose the phrase that best describes the shape of the sampling distribution 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.

Not normal because

n≤0.05N

and np(1−p)<10.

 

D.

Approximately normal because

n≤0.05N

and np(1−p)≥10.

 
Determine the mean of the sampling distribution of

p.
 
μp=nothing

​(Round to one decimal place as​ needed.)

 
Determine the standard deviation of the sampling distribution of

p.
 
σp=nothing

​(Round to six decimal places as​ needed.)

 
​(b) What is the probability of obtaining

x=55

or more individuals with the​ characteristic? That​ is, what is

​P(p≥0.44​)?
 
​P(p≥0.44​)=nothing

​(Round to four decimal places as​ needed.)

 
​(c) What is the probability of obtaining

x=40

or fewer individuals with the​ characteristic?

 
​P(p≤0.32​)=nothing

​(Round to four decimal places as​ needed.)

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