Question

These are the means and standard deviations for samples of prices from two

different brands of shoes

Brand A

Mean: $50

Standard deviation: $5

Brand B

Mean: $40

Standard deviation: $8

Select the two true statements,



A. Brand A has a higher average price than brand B.


B. Brand A's prices are more spread out than brand B's prices.


C. Brand A has a lower average price than brand B.


D. Brand A's prices are less spread out than brand B's prices,

Answer 1

A. Brand A has a higher average price than brand B.

D. Brand A's prices are less spread out than brand B's prices.

Explanation:

We are given the means and standard deviations for samples of prices from two different brands of shoes below;

Brand A Brand B

Mean : $50 Mean : $40

Standard deviation : $5 Standard deviation : $8

Now, from the given statements;

Statement A is correct that Brand A has a higher average price than brand B because as given above Mean of Brand A ($50) > Mean of Brand B ($40).

Also, Statement D is correct that Brand A's prices are less spread out than brand B's prices because the Variance of Brand A is less than the variance of Brand B, i.e.;

Variance of Brand A =
`5^(2)` = $25

Variance of Brand B =
`8^(2)` = $64

Clearly, $25 < $64, so statement D is also correct.

Therefore, the two true statements are Statement A and Statement D.