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Bernard randomly selected
10% of St. Francis citizens and asked them about their favorite coffee shop. Of the citizens surveyed, 7 said that Energize was their favorite coffee shop. Based on the data, what is the most reasonable estimate of the number of St. Francis citizens whose favorite coffee shop is Energize?
Choose 1 answer:
(A) 7
(B) 10
(c) 63
(D) 70

Bernard randomly selected $10 \%$ of St. Francis citizens and asked them about their favorite coffee shop. Of the citizens surveyed, $7$ said that Energize was their favorite coffee shop. Based on the data, what is the most reasonable estimate of the number of St. Francis citizens whose favorite coffee shop is Energize? $\newline$ Choose $1$ answer: $\newline$ (A) $7$ $\newline$ (B) $10$ $\newline$ (C) $63$ $\newline$ (D) $70$

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Experimental probability

Full solution

Q. Bernard randomly selected

10 \%

of St. Francis citizens and asked them about their favorite coffee shop. Of the citizens surveyed,

7

said that Energize was their favorite coffee shop. Based on the data, what is the most reasonable estimate of the number of St. Francis citizens whose favorite coffee shop is Energize?

\newline

Choose

1

answer:

\newline

(A)

7

\newline

(B)

10

\newline

(C)

63

\newline

(D)

70

Problem Understanding: First, we need to understand the problem. Bernard surveyed $10\%$ of St. Francis citizens, and $7$ of those surveyed said that Energize was their favorite coffee shop. We want to estimate the total number of citizens who prefer Energize based on this sample.
Setting up Proportion: Since $10$ % of the citizens were surveyed, and $7$ out of this group chose Energize, we can set up a proportion to find the total number of citizens who prefer Energize. Let's denote the total number of citizens in St. Francis as $x$ . The proportion is $\frac{7}{0.10x} = \frac{100\%}{x}$ .
Solving the Proportion: To find $x$ , we solve the proportion for $x$ . This gives us $x = \frac{7}{0.10}$ .
Calculating the Estimate: Calculating $x$ , we get $x = 7 \div 0.10 = 70$ . This means that the most reasonable estimate of the number of St. Francis citizens whose favorite coffee shop is Energize is $70$ .

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