The mean value of land and buildings per acre from a sample of farms is $1300, with a standard deviation of $200. 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)? $1616 $1774 $1309 $606 $1470 $1542

According to the empirical rule, when data is normally distributed (bell-shaped) then the values that are two standard deviations from the mean are unusual.

Given data: $1616 $1774 $1309 $606 $1470 $1542

Mean : [tex]\mu=\$1300[/tex] and Standard deviation: [tex]\sigma= \$200[/tex]

The range of the values lies within [tex]2\sigma[/tex] from mean [tex]\mu[/tex].

[tex](\mu-\2\sigma,\ \mu+2\sigma)\\\\=(1300-2(200),\ 1300+2(200))\\\\=(900,\ 1700)[/tex]

The values are unusual (i.e. more than two standard deviations from the mean) = $1774 and $606

The range of the values lies within [tex]3\sigma[/tex] from mean [tex]\mu[/tex].

[tex](\mu-\3\sigma,\ \mu+3\sigma)\\\\=(1300-3(200),\ 1300+3(200))\\\\=(700,\ 1900)[/tex]

The values are very unusual (i.e. more than three standard deviations from the mean) = $606