Question

the average price of commercial properties per square - foot in a metropolitan area is $2,000, with a standard deviation of $250. the data follows a bell - shaped distribution. estimate the percentage of commercial properties with prices per square foot between $1,750 and

Explanation:

1. Explanation:

• First, we need to use the z - score formula \(z=\frac{x - \mu}{\sigma}\), where \(\mu\) is the mean, \(\sigma\) is the standard deviation, and \(x\) is the value from the data set.
• Given that \(\mu = 2000\) (average price per square - foot), \(\sigma=250\) (standard deviation).
• For \(x = 1750\):
• Calculate the z - score: \(z_1=\frac{1750 - 2000}{250}=\frac{- 250}{250}=-1\).
• For \(x = 2250\) (since the problem seems to be incomplete but we assume the symmetric value around the mean for a bell - shaped distribution):
• Calculate the z - score: \(z_2=\frac{2250 - 2000}{250}=\frac{250}{250}=1\).
• According to the empirical rule (68 - 95 - 99.7 rule) for a normal (bell - shaped) distribution, approximately 68% of the data lies within \(z=-1\) and \(z = 1\).

1. Answer:

The percentage of commercial properties with prices per square - foot between \(1750\) and \(2250\) is approximately 68%.

Answer:

1. Explanation:

• First, we need to use the z - score formula \(z=\frac{x - \mu}{\sigma}\), where \(\mu\) is the mean, \(\sigma\) is the standard deviation, and \(x\) is the value from the data set.
• Given that \(\mu = 2000\) (average price per square - foot), \(\sigma=250\) (standard deviation).
• For \(x = 1750\):
• Calculate the z - score: \(z_1=\frac{1750 - 2000}{250}=\frac{- 250}{250}=-1\).
• For \(x = 2250\) (since the problem seems to be incomplete but we assume the symmetric value around the mean for a bell - shaped distribution):
• Calculate the z - score: \(z_2=\frac{2250 - 2000}{250}=\frac{250}{250}=1\).
• According to the empirical rule (68 - 95 - 99.7 rule) for a normal (bell - shaped) distribution, approximately 68% of the data lies within \(z=-1\) and \(z = 1\).

1. Answer:

The percentage of commercial properties with prices per square - foot between \(1750\) and \(2250\) is approximately 68%.