Question

the mean value of land and buildings per acre from a sample of farms is $1200, with a standard deviation of $300. the data - set has a bell - shaped distribution. using the empirical rule, determine which of the following farms, whose land and building values per acre are given, are unusual (more than two standard deviations from the mean). are any of the data values very unusual (more than three standard deviations from the mean)? $1034 $2069 $814 $267 $1057 $1511
which of the farms are unusual (more than two standard deviations from the mean)? select all that apply.
a. $267
b. $1511
c. $814
d. $1034
e. $1057
f. $2069

Explanation:

Step1: Calculate lower and upper bounds for unusual values

For a bell - shaped distribution, unusual values are more than two standard deviations from the mean. The mean $\mu = 1200$ and the standard deviation $\sigma=300$. The lower bound $L=\mu - 2\sigma=1200-2\times300 = 600$, and the upper bound $U=\mu + 2\sigma=1200 + 2\times300=1800$.

Step2: Check each data - value against bounds

For $1034$: $600<1034<1800$, not unusual.
For $2069$: $2069>1800$, unusual.
For $814$: $600<814<1800$, not unusual.
For $267$: $267<600$, unusual.
For $1057$: $600<1057<1800$, not unusual.
For $1511$: $600<1511<1800$, not unusual.

Answer:

A. $267$, F. $2069$