Question

The mean value of land and buildings per acre from a sample of farms is $1400, with a

standard deviation of $200.
The data set has a bell-shaped distribution. Assume the number of farms in the sample is 74.

(a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1000 and $1800.

___ farms (Round to the nearest whole number as needed.)

Answer 1

In this case, the mean is $1400, and the standard deviation is $200.

So, one standard deviation of the mean is 1400+200= $1600 and 1400-200 = $1200.

Therefore, according to the empirical rule, approximately 68% of the farms will have land and building values per acre between $1200 and $1600.

To estimate the number of farms that fall within this range, we can multiply the total number of farms (74) by 0.68.

(74)*(0.68) = 50.32 or about 50 farms

So, according to the empirical rule, approximately 50 farms will have land and building values per acre between $1000 and $1800.