If a sample of 100 residences has an average square footage of 1500 with a standard deviation of 120, what does this typically indicate about the homes?

The question revolves around the concept of standard deviation in a normal distribution. In a normally distributed dataset, we can use the empirical rule (also known as the 68-95-99.7 rule) to interpret the data.

According to this rule, about 68% of the data will fall within one standard deviation of the mean. In this case, the mean square footage of the residences is 1500 sq. ft., and the standard deviation is 120 sq. ft. Therefore:

• One standard deviation below the mean is 1500 - 120 = 1380 sq. ft.

• One standard deviation above the mean is 1500 + 120 = 1620 sq. ft.

This means that approximately 68% of the homes in the sample, or about 2 out of every 3 residences, have square footage between 1380 sq. ft. and 1620 sq. ft. This aligns precisely with the first choice, which accurately reflects the typical outcomes predicted by the empirical rule.

The other choices entail different ranges or percentages that do not align with the 68% threshold established by the empirical rule, thus they do not represent the typical distribution of square footage in this scenario.