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 unusual values (more than two standard deviations from the mean)

The formula for the range is \(\mu\pm2\sigma\), where \(\mu = 1200\) and \(\sigma=300\).
\(\mu - 2\sigma=1200-2\times300 = 600\)
\(\mu + 2\sigma=1200 + 2\times300=1800\)
Values less than \(600\) or greater than \(1800\) are unusual.
For \(249\lt600\) and \(1856>1800\), they are unusual.

Step2: Calculate the range for very unusual values (more than three standard deviations from the mean)

The formula for the range is \(\mu\pm3\sigma\), where \(\mu = 1200\) and \(\sigma = 300\)
\(\mu-3\sigma=1200-3\times300 = 300\)
\(\mu + 3\sigma=1200+3\times300=2100\)
Values less than \(300\) or greater than \(2100\) are very unusual.
Since \(249<300\) is not (as \(249\) is close to \(300\) but \(249\) is within the range of considering for two - standard - deviation first, and checking three - standard - deviation: \(1200-3\times300 = 300\), \(1200 + 3\times300=2100\). All given values \(1042,1856,1592,249,1032,926\) are within \((300,2100)\))

Answer:

Unusual: B. \(\$249\), F. \(\$1856\)
Very unusual: G. None of the data values are very unusual.