Final answer:
The distribution of sample proportions for a large sample size follows a normal distribution according to the central limit theorem for proportions.
The correct option is A
Step-by-step explanation:
To determine the distribution of sample proportions of U.S. adults with a college degree for random samples of size n, we need to consider the central limit theorem for proportions. The theorem states that if the sample size is sufficiently large, the sample proportion distribution P' follows a normal distribution with mean value p, representing the population proportion, and a standard deviation calculated as √(p*q/n), where q is the complementary probability (1 - p).
In the case of a large sample size (such as n = 1000), and based on statement (b) where P' = 0.2, we are dealing with a proportion problem where the outcomes are binary (Success/Failure). Applying the central limit theorem to this large sample size, we would expect the distribution to be normal.
In summary, among the given options, the correct choice would be that the distribution of sample proportions of U.S. adults with a college degree for random samples of size n...
- a. Follows a normal distribution
- b. Is skewed to the right
- c. Is skewed to the left
- d. Is uniform
Here, the most appropriate answer would be 'a. Follows a normal distribution', provided the sample size is large enough to apply the central limit theorem.
The correct option is A