Answer :
To determine the true statements, let's analyze the provided data for the two brands:
- Mean price of Brand A: \[tex]$50 - Mean price of Brand B: \$[/tex]40
- Standard deviation of Brand A: \[tex]$5 - Standard deviation of Brand B: \$[/tex]8
We will evaluate each statement one by one:
Statement A: Brand A's prices are more spread out than brand B's prices.
The "spread out" nature of prices is captured by the standard deviation. The standard deviation of Brand A is \[tex]$5, and the standard deviation of Brand B is \$[/tex]8. Since \[tex]$5 is less than \$[/tex]8, Brand A's prices are less spread out than Brand B's. Therefore, this statement is false.
Statement B: Brand A has a higher average price than Brand B.
The average price (mean) of Brand A is \[tex]$50, while the average price of Brand B is \$[/tex]40. Since \[tex]$50 is greater than \$[/tex]40, Brand A indeed has a higher average price than Brand B. Therefore, this statement is true.
Statement C: Brand A's prices are less spread out than brand B's prices.
As discussed in Statement A, the standard deviation of Brand A (\[tex]$5) is less than the standard deviation of Brand B (\$[/tex]8). Therefore, Brand A's prices are indeed less spread out than Brand B's prices. This statement is true.
Statement D: Brand A has a lower average price than Brand B.
The mean of Brand A is \[tex]$50, and the mean of Brand B is \$[/tex]40. Since \[tex]$50 is greater than \$[/tex]40, Brand A does not have a lower average price than Brand B. Therefore, this statement is false.
Based on the analysis, the true statements are:
- Statement B: Brand A has a higher average price than Brand B.
- Statement C: Brand A's prices are less spread out than Brand B's prices.
Therefore, the two selected true statements are B and C.
- Mean price of Brand A: \[tex]$50 - Mean price of Brand B: \$[/tex]40
- Standard deviation of Brand A: \[tex]$5 - Standard deviation of Brand B: \$[/tex]8
We will evaluate each statement one by one:
Statement A: Brand A's prices are more spread out than brand B's prices.
The "spread out" nature of prices is captured by the standard deviation. The standard deviation of Brand A is \[tex]$5, and the standard deviation of Brand B is \$[/tex]8. Since \[tex]$5 is less than \$[/tex]8, Brand A's prices are less spread out than Brand B's. Therefore, this statement is false.
Statement B: Brand A has a higher average price than Brand B.
The average price (mean) of Brand A is \[tex]$50, while the average price of Brand B is \$[/tex]40. Since \[tex]$50 is greater than \$[/tex]40, Brand A indeed has a higher average price than Brand B. Therefore, this statement is true.
Statement C: Brand A's prices are less spread out than brand B's prices.
As discussed in Statement A, the standard deviation of Brand A (\[tex]$5) is less than the standard deviation of Brand B (\$[/tex]8). Therefore, Brand A's prices are indeed less spread out than Brand B's prices. This statement is true.
Statement D: Brand A has a lower average price than Brand B.
The mean of Brand A is \[tex]$50, and the mean of Brand B is \$[/tex]40. Since \[tex]$50 is greater than \$[/tex]40, Brand A does not have a lower average price than Brand B. Therefore, this statement is false.
Based on the analysis, the true statements are:
- Statement B: Brand A has a higher average price than Brand B.
- Statement C: Brand A's prices are less spread out than Brand B's prices.
Therefore, the two selected true statements are B and C.
