To determine whether the student's sample is an appropriate, random sample and a good representation of the population, we need to consider a few factors:
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Random Selection: The student takes 15 ice samples from randomly selected coffee drinks. If the selection process is indeed random—meaning every coffee drink (and thus, its ice) had an equal chance of being selected—then it fulfills the random sampling criterion.
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Population Representation: To assess whether the sample represents the whole population, we must consider what "the population" refers to. If the population is defined as all the ice served at that coffee shop over time, then sampling only 15 drinks may not capture all variations (e.g., different times of day, different types of beverages, different employees handling the ice). However, if the sample adequately reflects the diversity of ice usage at the coffee shop within a reasonable time frame, it might still serve as a reasonable representation.
Given these considerations, if we assume the student has properly randomized her selection and if the 15 samples are adequately diverse in representing the ice served at the coffee shop, then you might select:
Option #1: Yes, her sample is an appropriate, random sample. It is a good representation of the population.
If, however, the method of sampling was flawed or if the samples do not effectively cover the diversity of the ice used, you would choose:
Option #2: No, her sample is not an appropriate, random sample. It does not represent the whole population.
Ultimately, further details about her sampling method and the population definition would clarify which option is more accurate.