Math Problem Statement

Use the results from a survey of a simple random sample of 1141 adults. Among the 1141 respondents, 74% rated themselves as above-average drivers. We want to test the claim that 13/20 of adults rate themselves as above-average drivers. Complete parts (a) through (c). (a) Identify the actual number of respondents who rated themselves as above-average drivers. (Round to the nearest whole number as needed.)

Solution

The question states that a survey of 1,141 adults found that 74% rated themselves as above-average drivers. The task is to calculate the actual number of respondents who rated themselves as above average.

Solution

  1. Total respondents = 1,141
  2. Percentage who rated themselves as above average = 74%

To find the number of respondents who rated themselves as above average, we calculate: Number of respondents=Total respondents×Percentage100\text{Number of respondents} = \text{Total respondents} \times \frac{\text{Percentage}}{100} =1141×74100= 1141 \times \frac{74}{100} =1141×0.74= 1141 \times 0.74 =844.34= 844.34

Since we are asked to round to the nearest whole number, the answer is: Answer=844\text{Answer} = 844

Final Answer

The actual number of respondents who rated themselves as above average drivers is 844.

Would you like further details or have any questions about the solution?


Here are five related questions to consider:

  1. What would be the number of respondents if only 60% rated themselves as above average?
  2. If the sample size increased to 2,000 with the same percentage, how many would rate themselves as above average?
  3. How would the answer change if the percentage increased to 80%?
  4. What is the percentage of respondents if 900 out of 1,141 rate themselves as above average?
  5. How could we calculate confidence intervals for the percentage of above-average drivers?

Tip: Always ensure you convert percentages to decimals before performing calculations!

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Math Problem Analysis

Mathematical Concepts

Percentage Calculation
Proportion
Rounding

Formulas

Number of respondents = Total respondents × (Percentage / 100)

Theorems

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Suitable Grade Level

Grades 10-12