Final answer:
The distribution of p' (sample proportion) is approximated by a normal distribution when the sample size is large enough and the conditions np > 5 and nq > 5 are met, where q = 1 - p. For large samples, a normal distribution is used to estimate proportions.
Step-by-step explanation:
The distribution of p' (sample proportion) can be approximated under certain conditions. When dealing with a proportion problem, you're often considering categorical data that indicates success or failure, yes or no responses. For a sample of size n, the distribution is approximately normal, according to the Central Limit Theorem, if the sample size is sufficiently large and the population proportion conditions are met (np > 5 and nq > 5, where q = 1 - p). If these conditions are satisfied, the distribution of the sample proportion p', where p' = x/n and x is the number of successes, can be denoted by N(p, sqrt(pq/n)). Additionally, if the binomial conditions are met but p is small and n is large, the Poisson distribution might be a suitable approximation. However, for estimating a proportion with a large n, and where p' is known, a normal distribution would be used, as depicted with P' = 0.2 and n = 1,000, resulting in a normal distribution N(0.2, sqrt((0.2)(0.8)/1000)).