Final answer:
The standard deviation/error of sample means for a population of 2, 4, 3, 7 with a sample size of 3 is approximately c) 1.08, as calculated using the Central Limit Theorem.
Step-by-step explanation:
The question is asking to calculate the standard deviation/error of sample means, given a population of 2, 4, 3, 7 and a fixed sample size of 3, based on the Central Limit Theorem. According to the theorem, the standard deviation of the sampling distribution of the sample means, also known as the standard error, is equal to the population standard deviation divided by the square root of the sample size (n). To find the correct answer, we first calculate the population standard deviation (σ). For our population (2, 4, 3, 7), the mean (μ) is (2+4+3+7)/4 = 4. The variance is calculated as [(2-4)^2 + (4-4)^2 + (3-4)^2 + (7-4)^2] / 4 = [4 + 0 + 1 + 9] / 4 = 3.5. Hence, the population standard deviation is the square root of 3.5, which is approximately 1.87. Then, we use the formula for the standard error of the mean: σ/√n. We have a sample size (n) of 3, so the standard error is 1.87/√3 ≈ 1.87/1.73, which is approximately 1.08. Therefore, the correct answer for the standard deviation/error of sample means is c) 1.08 according to the Central Limit Theorem.