Question

The mean value of land and buidings per acre from a sanple of farms is $1600, with a standard deviation of $300. The data sot has a bell-shaped distribution. Using the arrpirical rule, detarmine which of the following larms, whose land and buiding values per acre are given, are unusual (more than two standard deviatons from the mean). Ave any of the daca values very unusual (more than three standard devations from the mean)? $1606$2411$1344$573$1259$1043 Which of the fams are unutual (more than two standard deviations from the mean)? Select al that apply. A. $1608 B. 5573 C. $2411 D. $1259 E. $1344 F. 51043

Answer 1

To determine which of the given land and building values per acre are unusual (more than two standard deviations from the mean), you can use the empirical rule, also known as the 68-95-99.7 rule, which tells us that for a bell-shaped distribution:

- Approximately 68% of the data falls within one standard deviation from the mean.

- Approximately 95% of the data falls within two standard deviations from the mean.

- Approximately 99.7% of the data falls within three standard deviations from the mean.

Given that the mean is $1600, and the standard deviation is $300, you can calculate the values for two standard deviations and three standard deviations from the mean:

Two standard deviations from the mean:

Upper Limit = Mean + (2 * Standard Deviation) = $1600 + (2 * $300) = $2200

Lower Limit = Mean - (2 * Standard Deviation) = $1600 - (2 * $300) = $1000

Three standard deviations from the mean:

Upper Limit = Mean + (3 * Standard Deviation) = $1600 + (3 * $300) = $2500

Lower Limit = Mean - (3 * Standard Deviation) = $1600 - (3 * $300) = $700

Now, let's check each of the given values:

A. $1608: This value is within two standard deviations (between $1000 and $2200). Not unusual.

B. $573: This value is below two standard deviations (below $1000). Unusual.

C. $2411: This value is above two standard deviations (above $2200). Unusual.

D. $1259: This value is within two standard deviations (between $1000 and $2200). Not unusual.

E. $1344: This value is within two standard deviations (between $1000 and $2200). Not unusual.

F. $1043: This value is below two standard deviations (below $1000). Unusual.

So, the unusual values (more than two standard deviations from the mean) are:

B. $573

C. $2411

F. $1043

None of the given values are more than three standard deviations from the mean.

Explanation: