Question

Mimi value of land and buildings per acre from a sample of $1500 with a standard deviation of the data set has a bell-shaped distribution. Between what two values does 99.7% of the data lie?

Answer 1

Using the empirical rule, 99.7 percent of the data for a bell-shaped distribution lies within three standard deviations of the mean. For a mean value of $1500 and a standard deviation of $500, 99.7 percent of the data lies between $0 and $3000.

Step-by-step explanation:

The empirical rule states that for a bell-shaped distribution, about 68 percent of the data lies within one standard deviation of the mean, about 95 percent lies within two standard deviations, and about 99.7 percent lies within three standard deviations.

In the given problem, we have a mean value for land and buildings per acre of $1500 and a standard deviation of $500. To find the range where 99.7% of the data lies, we calculate three standard deviations above and below the mean:

• Lower limit = Mean - 3(Standard Deviation) = $1500 - 3($500) = $1500 - $1500 = $0
• Upper limit = Mean + 3(Standard Deviation) = $1500 + 3($500) = $1500 + $1500 = $3000

Therefore, 99.7 percent of the data lies between $0 and $3000.