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.