Let's analyze the given information and evaluate each statement based on the provided data:
1. Brand A:
- Mean price: \[tex]$50
- Standard deviation: \$[/tex]5
2. Brand B:
- Mean price: \[tex]$40
- Standard deviation: \$[/tex]8
### Statement Analysis
Statement A: Brand A has a lower average price than Brand B.
- We observe the mean prices for both brands. Brand A has a mean price of \[tex]$50, and Brand B has a mean price of \$[/tex]40.
- Since \[tex]$50 is greater than \$[/tex]40, Brand A does not have a lower average price than Brand B.
- Therefore, Statement A is false.
Statement B: Brand A's prices are less spread out than Brand B's prices.
- We look at the standard deviations to determine the spread. Brand A has a standard deviation of \[tex]$5, and Brand B has a standard deviation of \$[/tex]8.
- A smaller standard deviation indicates prices are less spread out.
- Since \[tex]$5 is less than \$[/tex]8, Brand A's prices are indeed less spread out than Brand B's prices.
- Therefore, Statement B is true.
Statement C: Brand A's prices are more spread out than Brand B's prices.
- Again, we refer to the standard deviations. Brand A's standard deviation is \[tex]$5, while Brand B's is \$[/tex]8.
- Since \[tex]$5 is smaller than \$[/tex]8, it cannot be said that Brand A's prices are more spread out than Brand B's prices.
- Therefore, Statement C is false.
Statement D: Brand A has a higher average price than Brand B.
- Reviewing the mean prices again, Brand A has a mean price of \[tex]$50, and Brand B has a mean price of \$[/tex]40.
- Since \[tex]$50 is greater than \$[/tex]40, Brand A indeed has a higher average price than Brand B.
- Therefore, Statement D is true.
### Conclusion
The two true statements, based on the analysis, are:
- Statement B: Brand A's prices are less spread out than brand B's prices.
- Statement D: Brand A has a higher average price than brand B.
The final answer is that the true statements are B and D.
