Questions: A random sample of 2,500 people was selected, and the people were asked to give their favorite season. Their responses, along with their age group, are summarized in the two-way table below. Winter Spring Summer Fall Total ---------------------------------------------- Children 30 0 170 0 200 Teens 150 75 250 25 500 Adults 250 250 250 250 1,000 Seniors 300 150 50 300 800 Total 730 475 720 575 2,500 Among those whose favorite season is spring, what proportion are adults? (A) 250/1,000 (B) 250/2,500 (C) 475/2,500 (D) 250/475 (E) 225/475

A random sample of 2,500 people was selected, and the people were asked to give their favorite season. Their responses, along with their age group, are summarized in the two-way table below. Winter Spring Summer Fall Total ---------------------------------------------- Children 30 0 170 0 200 Teens 150 75 250 25 500 Adults 250 250 250 250 1,000 Seniors 300 150 50 300 800 Total 730 475 720 575 2,500 Among those whose favorite season is spring, what proportion are adults? (A) 250/1,000 (B) 250/2,500 (C) 475/2,500 (D) 250/475 (E) 225/475
Transcript text: A random sample of 2,500 people was selected, and the people were asked to give their favorite season. Their responses, along with their age group, are summarized in the two-way table below. \begin{tabular}{|l|l|l|l|l|l|} \hline & Winter & Spring & Summer & Fall & Total \\ \hline Children & 30 & 0 & 170 & 0 & 200 \\ \hline Teens & 150 & 75 & 250 & 25 & 500 \\ \hline Adults & 250 & 250 & 250 & 250 & 1,000 \\ \hline Seniors & 300 & 150 & 50 & 300 & 800 \\ \hline Total & 730 & 475 & 720 & 575 & 2,500 \\ \hline \end{tabular} Among those whose favorite season is spring, what proportion are adults? (A) $\frac{250}{1,000}$ (B) $\frac{250}{2,500}$ (C) $\frac{475}{2,500}$ (D) $\frac{250}{475}$ (E) $\frac{225}{475}$
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Solution

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Solution Steps

Step 1: Identify the relevant data

From the two-way table, we are interested in the proportion of adults among those whose favorite season is spring. The number of adults who prefer spring is 250, and the total number of people who prefer spring is 475.

Step 2: Calculate the proportion

The proportion of adults among those who prefer spring is calculated as: \[ \text{Proportion} = \frac{\text{Number of adults who prefer spring}}{\text{Total number of people who prefer spring}} = \frac{250}{475}. \]

Step 3: Match the proportion with the given options

The calculated proportion \(\frac{250}{475}\) matches option (D).

Final Answer

\(\boxed{\text{D}}\)

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