Question

Describe the sampling distribution of ModifyingAbove p with caret. Assume the size of the population is 20,000. n=500​, p=0.2 Choose the phrase that best describes the shape of the sampling distribution of ModifyingAbove p with caret below.

A. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10.

B. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10.

C. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10.

D. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10.

Determine the mean of the sampling distribution:____

Determine the standard deviation of the sampling distribution:____

Answer 1

Solution :

p = 0.2

1 - p = 0.8

n = 500

N = 20000

n 0.05 N

500 0.05 * 20000

500 1000

Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p

right parenthesis greater than or equals 10.

The mean of the sampling distribution of proportion is ,

= p = 0.2

The standard deviation of the sampling distribution is ,  

=  [p( 1 - p ) / n = [(0.2 * 0.8) / 500 ] = 0.0179