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These are the means and standard deviations for samples of prices from two different brands of shoes.

\begin{tabular}{|c|c|}
\hline Brand A & Brand B \\
\hline Mean: \[tex]$50 & Mean: \$[/tex]40 \\
\hline Standard deviation: \[tex]$5 & Standard deviation: \$[/tex]8 \\
\hline
\end{tabular}

Select the two true statements.

A. Brand A's prices are more spread out than brand B's prices.
B. Brand A has a higher average price than brand B.
C. Brand A's prices are less spread out than brand B's prices.
D. Brand A has a lower average price than brand B.

Sagot :

GinnyAnswer
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.
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