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The mayor surveyed the first $15$ people to arrive for a town meeting. $\newline$ Is this sample of the residents of the town likely to be representative? $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Experimental probability

Full solution

Q. The mayor surveyed the first

15

people to arrive for a town meeting.

\newline

Is this sample of the residents of the town likely to be representative?

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Understand the problem: Step $1$ : Understand the problem. $\newline$ The mayor wants to know if the first $15$ people at a town meeting represent the whole town. We need to think about what ＂representative＂ means in statistics.
Analyze sample size: Step $2$ : Analyze the sample size and diversity. $\newline$ $15$ people is a very small number compared to a whole town's population. Usually, a representative sample should be larger and randomly selected to reflect the entire population's diversity in age, gender, race, and more.
Make decision: Step $3$ : Make a decision based on statistical principles. $\newline$ Since the sample is small and not randomly selected, it's unlikely to represent the whole town accurately.

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