In Exercises 37–44, answer the given questions, which are related to percentages.
Marriage Proposals In a survey conducted by TheKnot.com, 1165 engaged or married women were asked about the importance of a bended knee when making a marriage proposal. Among the 1165 respondents, 48% said that the bended knee was essential.


a. What is the exact value that is 48% of 1165 survey respondents?
b. Could the result from part (a) be the actual number of survey subjects who said that a bended knee is essential? Why or why not?

Verified step by step guidance

1. To find the exact value that is 48% of 1165 survey respondents, you need to calculate 48% of 1165. This can be done by multiplying 1165 by 0.48. In MathML, this calculation can be represented as: $1165\times 0.48$.
2. Perform the multiplication to find the number of respondents who said that a bended knee was essential. This will give you the exact number of respondents.
3. For part (b), consider whether the result from part (a) could be the actual number of survey subjects. Since the number of respondents must be a whole number, check if the result from part (a) is an integer.
4. If the result from part (a) is not an integer, explain why it cannot be the actual number of survey subjects. Discuss the concept of rounding and how percentages can result in non-integer values when applied to a total number.
5. Conclude by discussing the implications of rounding in survey results and how it affects the interpretation of data, emphasizing the importance of understanding the limitations of percentage calculations in real-world scenarios.

Key Concepts

Percentage Calculation

Percentage calculation involves determining a portion of a whole expressed as a fraction of 100. To find the exact value that corresponds to a given percentage, you multiply the total number by the percentage (in decimal form). In this case, to find 48% of 1165, you would calculate 1165 * 0.48, which gives the number of respondents who consider the bended knee essential.

Sample Size and Representation

Sample size refers to the number of individuals surveyed or studied in a research project. In this context, the sample size is 1165 women. Understanding sample size is crucial because it affects the reliability and validity of the survey results. A larger sample size generally provides a more accurate representation of the population, while a smaller sample may lead to skewed results.

Interpreting Survey Results

Interpreting survey results involves analyzing the data collected to draw conclusions about the population. In part (b) of the question, one must consider whether the calculated number of respondents (from part a) aligns with the survey's context and methodology. It's important to assess if the percentage reflects a significant sentiment among the surveyed group and whether the sample is representative of the broader population.