Final answer:
Based on the provided details of the sampled normal distribution, the estimate with a mean of 28 and a standard deviation of 4 best matches the given scenario, due to the known standard deviation and properties of normal distributions. The correct answer is option 1.
Step-by-step explanation:
When estimating the mean and standard deviation of a normal distribution, it's important to remember that the mean (μ) is the central value around which the density curve is symmetrical, and the standard deviation (σ) is a measure of the spread of the data points around the mean. In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and about 99.7% falls within three standard deviations. Given the scenario that samples are drawn from a normally distributed population for which we know the standard deviation but not the mean, we can estimate these parameters based on the sample data and the properties of the normal distribution.
In the datasets provided: For a sample of size 30 from a normally distributed population with a standard deviation of four, a population with a mean of 125 and a standard deviation of seven, we can match one of the options presented in the question. The correct option with an estimated mean of 28 and a standard deviation of 4 corresponds to the information given about the sample size and standard deviation of the population from which the sample is drawn.
Therefore, the correct option is: Mean = 28, Standard deviation = 4.