the mean - value of land and buildings per acre from a sample of farms is $1200, with a standard deviation…

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. $1957$