Question

here are some summary statistics for the numbers of acres of soybeans and peanuts harvested per county in alabama in 2009, for counties that planted those crops.

crop	mean harvest (thousands of acres)	standard deviation (thousands of acres)
peanuts	$mu = 10$	$sigma = 8$

in one southern county, there were 9 thousand acres of soybeans harvested and 3 thousand acres of peanuts harvested.

relative to its crop, which plant had a better harvest?

Explanation:

Step1: Calculate z - score for soybeans

The z - score formula is $z=\frac{x-\mu}{\sigma}$. For soybeans, $x = 9$, $\mu=12$, and $\sigma = 14$. So $z_{soybeans}=\frac{9 - 12}{14}=\frac{- 3}{14}\approx - 0.214$.

Step2: Calculate z - score for peanuts

For peanuts, $x = 3$, $\mu = 10$, and $\sigma=8$. So $z_{peanuts}=\frac{3 - 10}{8}=\frac{-7}{8}=-0.875$.

Step3: Compare z - scores

The higher the z - score (less negative in case of negative z - scores), the better the harvest relative to the mean of its crop. Since $-0.214>-0.875$, soybeans had a better harvest relative to its crop.

Answer:

Soybeans