A simple random sample (SRS) of 125 is taken from a population with a 0.2 proportion of success. An independent SRS of 175 is taken from a population with a 0.9 proportion of success. What is the standard deviation of the sampling distribution for the difference in sample proportions?

A) 0.0424
B) 0.0497
C) 0.0018
D) 0.0245
E)None of the above

And the best option would be:

A) 0.0424

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

represent the real population proportion for the first case A

represent the proportion for case A

is the sample size selected for A

represent the real population proportion for case B

represent the estimated proportion for case B

is the sample size required for case B

represent the critical value for the margin of error  

Solution to the problem

The population individual proportion have the following distribution  

And the standard deviation for the difference of proportions woud be given by:

And replacing we got:

And the best option would be:

A) 0.0424

probability for j is 1/4

while

a is 1/6