The figure shows how the distribution of a sampling proportion appears when the sample size is n=10 , n=100 , and n=1000 . How does the range of variability and the shape of the distribution change as the sample size becomes larger? (1 point) Responses As the sample size increases, the range of variability decreases, and the shape of the distribution becomes more symmetric. As the sample size increases, the range of variability decreases, and the shape of the distribution becomes more symmetric. As the sample size increases, the range of variability increases, and the shape of the distribution becomes more symmetric.
1 answer
The correct response is: As the sample size increases, the range of variability decreases, and the shape of the distribution becomes more symmetric.
As the sample size increases, the variability in the sampling distribution of the sample proportion tends to decrease, leading to a narrower range. Additionally, according to the Central Limit Theorem, the distribution of the sampling proportion becomes more symmetric and approaches a normal distribution as the sample size increases.
