Question

About of the homes will be priced between $150,000 and $225,000.

Answer 1

About 99.7% of the homes will be priced between $150,000 and $225,000 in this Denver neighborhood.

Let's approach this step by step:

Determine the Z-scores: Z-score is a measure of how many standard deviations a particular data point is from the mean in a normal distribution. The formula for Z-score is given by:


`Z = (X - Mean) / Standard Deviation`

For the lower limit of $150,000:

`Z_Lower = (150,000 - 187,500) / 12,500`

For the upper limit of $225,000:

`Z_ Upper = (225,000 - 187,500) / 12,500`

Use Z-table or Calculator: Look up or calculate the percentage of data within these Z-scores. A standard normal distribution table or calculator will provide this information.

Calculate the Percentage: Subtract the percentage corresponding to the lower Z-score from the percentage corresponding to the upper Z-score to find the percentage between them.

Final Answer: Use the percentage calculated to complete the statement.

Let's proceed with the calculations:

`Z_Lower = (150,000 - 187,500) / 12,500 = -3`

`Z_Upper = (225,000 - 187,500) / 12,500 = 3`

Using a standard normal distribution table or calculator, find the percentages for Z = -3 and Z = 3. This gives the percentage of data within one standard deviation of the mean. Let's assume you find that about 99.7% of the data is within this range.

Percentage between $150,000 and $225,000 = 99.7%

Answer 2

About 99.73% of the homes in the Denver neighborhood will be priced between $150,000 and $225,000.

We are going to use the properties of the normal distribution to find the proportion of homes priced between $150,000 and $225,000 in the Denver neighborhood.

The z-scores for the lower and upper bounds of the price range will be computed.

For the lower bound:

Z_lower = (X_lower - μ) / σ

= (150,000 - 187,500) / 12,500

= -3

For the upper bound:

Z_upper = (X_upper - μ) / σ

= (225,000 - 187,500) / 12,500

= 3

Using table, the area between z = -3 and z = 3 is 0.9973.

Therefore, about 99.73% of the homes in the Denver neighborhood will be priced between $150,000 and $225,000.

Full question:

Real estate prices in a Denver neighborhood are Normally distributed with a mean price of $187,500 and a standard deviation of $12,500.

A graph titled Denver Neighborhood Real Estate Pricing has Cost (dollars) on the x-axis, going from 150,000 to 225,000 in increments of 12,500. The highest point of the curve is at 187,500.

Complete the statement based on this information.

About __ of the homes will be priced between $150,000 and $225,000.