Question

the mean - value of land and buildings per acre from a sample of farms is $1200, with a standard deviation of $200. the data set has a bell - shaped distribution. using the sample 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 very unusual (more than three standard deviations from the mean)? $1054 $2299 $814 $807 $1987 $1511
which of the farms are unusual (more than two standard deviations from the mean)? select all that apply.
a. $807
b. $1511
c. $814
d. $1054
e. $1987
f. $2299
which of the farms are very unusual (more than three standard deviations from the mean)? select all that apply.
a. $1987
b. $1511
c. $807
d. $814
e. $2299
f. $1054
g. none of the data values are very unusual.

Explanation:

Step1: Recall the range for usual and very - unusual values

Unusual values are more than 2 standard deviations from the mean, and very - unusual values are more than 3 standard deviations from the mean. Let the mean $\mu = 1266$ and the standard deviation $\sigma=226$.
The range for usual values is $\mu - 2\sigma\leq x\leq\mu + 2\sigma$ and for very - usual values is $\mu - 3\sigma\leq x\leq\mu + 3\sigma$.
First, calculate $\mu - 2\sigma=1266-2\times226 = 1266 - 452=814$ and $\mu + 2\sigma=1266 + 452 = 1718$.
Then, calculate $\mu - 3\sigma=1266-3\times226=1266 - 678 = 588$ and $\mu + 3\sigma=1266+678 = 1944$.

Step2: Check each value for unusualness

For $x = 807$, since $807<814$, it is unusual (more than 2 standard deviations from the mean).
For $x = 1511$, since $814<1511<1718$, it is not unusual.
For $x = 814$, it is at the boundary of the usual range, so it is not unusual.
For $x = 1024$, since $814<1024<1718$, it is not unusual.
For $x = 1957$, since $1957>1944$, it is very unusual (more than 3 standard deviations from the mean).
For $x = 1299$, since $814<1299<1718$, it is not unusual.

Answer:

Which of the farms are unusual (more than two standard deviations from the mean)? Select all that apply:
A. $807$
F. $1957$

Which of the farms are very unusual (more than three standard deviations from the mean)? Select all that apply:
A. $1957$