Question

These are the means and standard deviation for samples of building heights in two different cities. Select the two true statements.

Answer 1

The two true statements are A. City A's heights are more spread out than B and C. City A has a lower average height than B

Explanation:

• The mean for building heights in city A is 120 feet while in city B it is 200 feet. This means that if all the heights are summed with each other and this sum is divided by the number of buildings measured we get 120 feet in city A and get 200 feet in city B. So buildings in city B have a higher average height than the buildings in city A. So Option C is true.
• City A has a standard deviation of 20 feet while city B's is 12 feet. This standard deviation means that the majority of buildings heights are within 20 feet in city A and 12 feet in city B. Combining both sets of data, we can say that most of city A's building heights are within 100 and 140 feet. For city B most of the building heights are within 188 feet and 212 feet. So City A has more spread than City B which is option A.