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 which of the farms are very unusual (more than three standard deviations from the mean)? select all that apply. a. $926 b. $249 c. $1592 d. $1856 e. $1032 f. $1042 g. none of the data values are very unusual

Explanation:

Step1: Calculate the range for two - standard deviations

The mean \(\mu = 1200\) and the standard deviation \(\sigma=300\).
The lower bound for two - standard deviations is \(\mu - 2\sigma=1200-2\times300 = 1200 - 600=600\).
The upper bound for two - standard deviations is \(\mu + 2\sigma=1200 + 2\times300=1200 + 600 = 1800\).

Step2: Check each value for two - standard deviations

• For \(x = 1042\): \(600<1042<1800\)
• For \(x = 1856\): \(1856>1800\)
• For \(x = 1592\): \(600<1592<1800\)
• For \(x = 249\): \(249<600\)
• For \(x = 1032\): \(600<1032<1800\)
• For \(x = 926\): \(600<926<1800\)

Step3: Calculate the range for three - standard deviations

The lower bound for three - standard deviations is \(\mu-3\sigma=1200 - 3\times300=1200-900 = 300\).
The upper bound for three - standard deviations is \(\mu + 3\sigma=1200+3\times300=1200 + 900=2100\).

Step4: Check each value for three - standard deviations

• For \(x = 1042\): \(300<1042<2100\)
• For \(x = 1856\): \(300<1856<2100\)
• For \(x = 1592\): \(300<1592<2100\)
• For \(x = 249\): \(249<300\)
• For \(x = 1032\): \(300<1032<2100\)
• For \(x = 926\): \(300<926<2100\)

Answer:

Which of the farms are unusual (more than two standard deviations from the mean)? Select all that apply:
B. \(\$249\), F. \(\$1856\)

Which of the farms are very unusual (more than three standard deviations from the mean)? Select all that apply:
G. None of the data values are very unusual