Final answer:
The correct answer is D.The student's question is about using the empirical rule, an inferential statistics concept, to estimate the land and building values of farms. The question involves statistical analysis, estimation techniques, and interpretation of the sample data and the greater population.
Step-by-step explanation:
Understanding Inferential Statistics
When we refer to the empirical rule or 68-95-99.7 rule, we are discussing a concept in statistics that relates to the normal distribution.
Specifically, this rule states that for a normal distribution, approximately 68% of the data will fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
In this scenario, given the average size of a U.S. farm in 1940 was 174 acres with a standard deviation of 55 acres, if we survey 38 farmers, we can estimate the percentage of farms within a certain range
This process is a part of inferential statistics, which involves using sample data to infer information about the greater population.
Furthermore, when the question asks to estimate the number of farms based on these data points, it is utilizing estimation techniques to make predictions about the population parameter from the sample .
In this case, the sample mean
and the sample size are used to draw conclusions about the population mean (μ).
The goal of such an analysis is to allow statisticians to predict with a certain level of confidence what might be expected in the overall population based on a smaller, random sample.
These techniques are fundamental for statistical analysis, probability distribution calculation, and data interpretation.