The Centers for Disease Control and Prevention (CDC) tracks cancer incidence rates for most cancer types across all 50 states. In 2014, the CDC found that the proportion of adults with breast cancer in Nevada was 0.00010660.0001066, and the proportion of adults with breast cancer in Illinois was 0.00013350.0001335. Suppose that in 2014, a random sample of 20002000 adults is taken from Nevada and a random sample of 10001000 adults is taken from Illinois.Suppose the CDC then wish to conduct a two‑proportion zz‑test to determine if the difference in proportions is statistically significant. Assume that all conditions for this two‑proportion zz‑test have been met. The standard error (SE) for this test is 0.00041630.0004163. Which of these distributions accurately represents the sampling distribution of the difference in sample proportions for this two‑proportion zz‑test?
a) approximately normally distributed with mean 0 and standard deviation 1
b) approximately normally distributed with mean 0.0002401 and standard deviation 0.0004163
c) approximately normally distributed with mean -0.0000269 and standard deviation 0.0004163
d) approximately normally distributed with mean-0.0000269 and standard deviation 1