Question

raquel and van live in two different cities. as part of a project, they each record the lowest prices for a gallon of gas at gas stations around their cities on the same day. raquels data show $\bar{x}=3.42$ and $sigma = 0.07$. vans data show $\bar{x}=3.78$ and $sigma = 0.23$. which statement is true about their gas - price data? raquels data are most likely closer to $3.42 than vans data are to $3.78. vans data are most likely closer to $3.42 than raquels data are to $3.78. raquels data are most likely closer to $3.78 than vans data are to $3.42. vans data are most likely closer to $3.78 than raquels data are to $3.42.

Explanation:

Step1: Understand standard - deviation concept

Standard - deviation ($\sigma$) measures the amount of variation or dispersion of a set of values. A smaller standard - deviation indicates that the data points tend to be closer to the mean ($\bar{x}$), while a larger standard - deviation indicates that the data points are more spread out from the mean.

Step2: Compare standard - deviations

Raquel's data has a mean $\bar{x}_R = 3.42$ and standard - deviation $\sigma_R=0.07$. Van's data has a mean $\bar{x}_V = 3.78$ and standard - deviation $\sigma_V = 0.23$. Since $\sigma_R=0.07<\sigma_V = 0.23$, Raquel's data points are more likely to be closer to her mean value of $3.42$ compared to Van's data points being close to his mean value of $3.78$.

Answer:

Raquel's data are most likely closer to $3.42$ than Van's data are to $3.78$.