Question

The mean value of land and buildings per acre from a sample of farms is $1700, with a standard deviation of $200.

The data set has a bell-shaped distribution. Assume the number of farms in the sample is 71.

(a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between
$1300 and $2100.

___farms (Round to the nearest whole number as needed.)

Answer 1

The empirical rule states that for a bell-shaped distribution, approximately 68% of the data will fall within one standard deviation of the mean, approximately 95% of the data will fall within two standard deviations of the mean, and approximately 99.7% of the data will fall within three standard deviations of the mean.

In this case, the mean is $1700 and the standard deviation is $200.

So, one standard deviation of the mean is 1700+200= $1900 and 1700-200 = $1500.

Therefore, according to the empirical rule, approximately 68% of the farms will have land and building values per acre between $1500 and $1900.

To estimate the number of farms that fall within this range, we can multiply the total number of farms (71) by 0.68.

(71)*(0.68) = 48.68 or about 49 farms

So, according to the empirical rule, approximately 49 farms will have land and building values per acre between $1300 and $2100.