Question

The USDA’s 2017 Census of Agriculture report, Louisiana’s Market Value of Agricultural Products Sold, found a total value of production of $3.173 billion on 27,400 farms (both measures exclude forestry production but include Christmas trees, tree fruits, and tree nuts). Suppose, then, the typical farm’s value of production was ? = $115,860 [$3,172,978,000 / 27,386 farms = $115,860 per farm]. The range of these data was found to be $47,080 per farm. Assume a normal distribution. Given P (x < Farm_Sales) = 0.7500, what is Farm_Sales to the nearest dollar? In other words, at what sales level are 75% of the farms below? Interpret your answer in the context of the problem to the nearest dollar.

Answer 1

Solution:

We are given:

Now to find the sales level which is 75% of the farms below, we first need to find the z-value corresponding to area = 0.75. Using the standard normal table, we have:

Now using the z-score formula, we have:

Therefore, at $123793 sales, there are 75% of the farms below