The mean value of land and building 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)?
As stated in the question, two standard deviations from the mean constitutes unusual values,
$$(\$1200 - 2\times \$300, \$1200+2\times\$300) = (\$600,\$1800)$$
therefore any values falling outside this range would be considered unusual. \$293 and \$1928 are both unusual.
Three standard deviations from the mean constitute very unusual values,
$$(\$1200 - 3\times \$300, \$1200+3\times\$300) = (\$300,\$2100)$$
The only value that is highly unusual is $293.
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