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)? $1042 $1856 $1592 $249 $1032 $926 which of the farms are unusual (more than two standard deviations from the mean)? select all that apply. a. $1592 b. $249 c. $1042 d. $1032 e. $926 f. $1856

Explanation:

Step1: Calculate the range for non - unusual values (within two standard deviations)

The formula for the range is \(\mu - 2\sigma\) to \(\mu+2\sigma\), where \(\mu = 1200\) (mean) and \(\sigma=300\) (standard deviation).
\(\mu - 2\sigma=1200-2\times300 = 1200 - 600=600\)
\(\mu + 2\sigma=1200 + 2\times300=1200 + 600 = 1800\)

Step2: Check each data value against the range

• For \(A\): \(600<1592<1800\), so it is not unusual.
• For \(B\): \(249<600\), so it is unusual.
• For \(C\): \(600<1042<1800\), so it is not unusual.
• For \(D\): \(600<1032<1800\), so it is not unusual.
• For \(E\): \(600<926<1800\), so it is not unusual.
• For \(F\): \(1856>1800\), so it is unusual.

Answer:

B. \(\$249\), F. \(\$1856\)