Describe the sampling distribution of p with caret. Assume the size of the population is 30,000. n=400, p=0.6 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. Not normal because n≥0.05
N and
np(1−p)<10.
D. Approximately normal because n≤0.05N and np(1−p)≥10.
The mean of the sampling distribution of p with caret is the same as the population proportion. Determine the standard deviation of the sampling distribution of p with a caret.

The correct option is D

The  standard deviation is mathematically represented as

Step-by-step explanation:

From the question we are told that

       The  population size is  

       The  sample  size is  

       The  population proportion is  

Generally for the sampling distribution of   to be  normal  

and  

Now  testing we have that

So

Now  let test the next condition

So

Given that the  sampling distribution of meets the above requirement it mean that the shape is normal

  Generally the standard deviation of the sampling distribution of is mathematically represented as

=>    

=>