The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 107 pounds and a standard deviation of 39.3 pounds. Random samples of size 18 are drawn from this population, and the mean of each sample is determined.

The question involves the application of normal distribution and sample means in statistics to analyze per capita red meat consumption. The context provided includes dietary trend changes over time, reflecting shifts in consumer preferences and demand curves.

Explanation:

The student's question pertains to the normal distribution of red meat per capita consumption, a statistical concept used in mathematics to describe how values are spread around a mean. Based on a given mean of 107.107 pounds and a standard deviation of 39.339.3 pounds, we would analyze sample means for groups of 18 individuals. To do this, we use the Central Limit Theorem which states that the sampling distribution of the sample mean will be normally distributed if the sample size is large enough, typically n > 30, but even smaller samples from a normal population will be approximately normal.

As per the historical data from the USDA, we observe changes in per-capita consumption trends for chicken and beef, indicating shifts in consumer preferences affecting the demand curve over time. This information provides context to the type of data involved but does not directly affect the statistical analysis of sample means asked in the question.

Moreover, these statistical concepts could be used to estimate population parameters and analyze shifts in dietary patterns as suggested by the change in the consumption of chicken and beef over the years.