Question

the median boiling temperature of the tap water is 100°c. the median boiling temperature of the salt water is 102°c. which statement about the means is most likely true? the mean of the tap water boiling temperatures is about 4° less than the mean of the saltwater boiling temperatures. the mean of the tap water boiling temperatures is about 2° less than the mean of the saltwater boiling temperatures. the mean of the tap water boiling temperatures is about 1° greater than the mean of the saltwater boiling temperatures. the mean of the tap water boiling temperatures is about 3° less than the mean of the saltwater boiling temperatures.

Explanation:

Step1: Analyze the median - mean relationship

In general, for a right - skewed distribution, the mean is greater than the median, and for a left - skewed distribution, the mean is less than the median. Since the median boiling temperature of tap water is \(100^{\circ}C\) and of salt water is \(102^{\circ}C\), and considering typical properties of salt water having a higher boiling point on average.

Step2: Estimate the mean difference

Based on common knowledge of the effect of salt on the boiling point of water, the mean boiling point of salt water is higher than that of tap water. Looking at the options, a difference of around \(2^{\circ}C\) is a reasonable estimate considering the median values and the nature of the substances.

Answer:

The mean of the tap water boiling temperatures is about \(2^{\circ}\) less than the mean of the saltwater boiling temperatures.