Question

It is known that 4% of computer chips in a large shipment are defective. Let the sample proportion be the proportion of defectives in a random sample of n = 2000 chips from the shipment. What is the sampling distribution of the sample proportion?

It is known that 4% of computer chips in a large shipment are defective. Let the sample proportion be the proportion of defectives in a random sample of n = 2000 chips from the shipment. What is the sampling distribution of the sample proportion? Select one: a. It is at least approximately normal with a standard deviation of 0.00438. O b. It is right-skewed with a standard deviation of 0.000894. O c. It is at least approximately normal with a standard deviation of 0.0000192. O d. It is at least approximately normal with a standard deviation of 0.000894. o e. It is at least approximately normal with a standard deviation of 0.04.

Answer 1

Solution:

p = 4% = 0.04

n = 2000

n * p = 2000 * 0.04 = 80

n * (1 - p) = 1920

Both are greater than 10. So sampling distribution of sample proportion is approximately normal.

The sampling distribution of $\hat p$ is approximately normal with

mean = $\mu_{\hat p}$ =  p = 0.04

SD = $\sigma_{\hat p}$   =     

=  

0.04(1 -0.04)/2000

=  0.00438

Answer :

It is at least approximately normal with a standard deviation of 0.00438