Final answer:
The model for the sample proportion of residents living below the poverty line follows a normal distribution for a single proportion, determined by the population proportion and the sample size. The standard deviation is calculated using the formula σ = √[(p * q) / n] and one needs to find the option where the standard deviation is closest to the calculated one.
Step-by-step explanation:
The model that the sample proportion of residents who are living below the poverty line follows is a normal distribution for a single proportion. To determine which of the given options is correct, we would need to calculate the standard deviation of the sampling distribution of the sample proportion based on the population proportion and the sample size. The formula for the standard deviation (σ) of a sample proportion is:
σ = √[(p * q) / n]
where p is the population proportion, q is 1 - p, and n is the sample size. Given the additional information, if we assume that P' = 0.2 (which is close to 0.18) and n = 1,000, we would use:
σ = √[(0.2 * 0.8) / 1000] = √[0.16 / 1000] = √[0.00016] = 0.0126
The nearest option to our calculated standard deviation is 'c. n(0.18, 0.00300)' which seems to be a typo because 0.00300 is substantially smaller than our calculated 0.0126. Nevertheless, the key point is that we're dealing with a normal distribution based on the central limit theorem which states that the sampling distribution of the sample proportion will be approximately normal if the sample size is large enough.
We're unable to verify the exact option without precise values but we can deduce that the valid model should be a normal distribution with a mean equal to the population proportion and a standard deviation calculated as shown above.