Determining Range of Prices in Scenario 2

Question:

Given the mean price of new homes and standard deviation in Scenario 2, between what two prices do 95% of the new homes fall?

a. $120,000 and $180,000

b. $135,000 and $180,000

c. $135,000 and $165,000

d. $105,000 and $195,000

Answer:

To determine between what two prices 95% of the new homes fall in Scenario 2, we can use the concept of the normal distribution and z-scores.

Given that the data set has a bell-shaped distribution, we can apply the empirical rule, also known as the 68-95-99.7 rule. According to this rule, approximately 95% of the data falls within two standard deviations of the mean in a bell-shaped distribution.

In Scenario 2, the mean price of new homes is $150,000 with a standard deviation of $15,000. Therefore, we can calculate the range within two standard deviations of the mean as follows:

Lower Limit: Mean - (2 * Standard Deviation) = $150,000 - (2 * $15,000) = $120,000

Upper Limit: Mean + (2 * Standard Deviation) = $150,000 + (2 * $15,000) = $180,000

So, between $120,000 and $180,000, approximately 95% of the new homes' prices would fall.

Therefore, the correct answer is a. $120,000 and $180,000.