To find the two true statements given the means and standard deviations for the building heights in City A and City B, let's analyze each statement one by one.
1. Analysis of Statement A:
"City A's heights are less spread out than City B's heights."
- City A's standard deviation: 20 ft
- City B's standard deviation: 12 ft
The standard deviation is a measure of how spread out the values are around the mean. Since City A has a standard deviation of 20 ft, and City B has a standard deviation of 12 ft, the heights in City A are actually more spread out compared to City B. Therefore, this statement is false.
2. Analysis of Statement B:
"City A has a lower average height than City B."
- City A's mean height: 120 ft
- City B's mean height: 240 ft
The average or mean height of buildings in City A is 120 ft, which is less than the average height of 240 ft in City B. Therefore, this statement is true.
3. Analysis of Statement C:
"City A's heights are more spread out than City B's heights."
- City A's standard deviation: 20 ft
- City B's standard deviation: 12 ft
As previously mentioned, standard deviation quantifies the amount of variation or dispersion around the mean. Since City A has a standard deviation of 20 ft, which is greater than City B's standard deviation of 12 ft, City A's heights are indeed more spread out than City B's heights. Therefore, this statement is true.
4. Analysis of Statement D:
"City A has a greater average height than City B."
- City A's mean height: 120 ft
- City B's mean height: 240 ft
The average height in City A (120 ft) is less than the average height in City B (240 ft). Consequently, this statement is false.
Summarizing our findings:
- Statement A is false.
- Statement B is true.
- Statement C is true.
- Statement D is false.
Thus, the two true statements are:
- [tex]\(\boldsymbol{\text{B. City A has a lower average height than City B.}}\)[/tex]
- [tex]\(\boldsymbol{\text{C. City A's heights are more spread out than City B's heights.}}\)[/tex]
