Math Problem Statement

Use the results from a survey of a simple random sample of 1224 adults. Among the 1224 ​respondents, 85​% rated themselves as above average drivers. We want to test the claim that four fifths of adults rate themselves as above average drivers. Complete parts​ (a) through​ (c).

Question content area bottom

Part 1 a. Identify the actual number of respondents who rated themselves as above average drivers.

Solution

To find the actual number of respondents who rated themselves as above average drivers, we use the percentage provided and apply it to the total number of respondents.

Given:

  • Total number of respondents = 1224
  • Percentage who rated themselves as above average drivers = 85%

Now calculate:

Number of respondents who rated themselves as above average=1224×(85100)=1224×0.85\text{Number of respondents who rated themselves as above average} = 1224 \times \left(\frac{85}{100}\right) = 1224 \times 0.85

Number of respondents=1040.4\text{Number of respondents} = 1040.4

Since the number of respondents must be a whole number, we round it to:

Number of respondents=1040\text{Number of respondents} = 1040

Thus, 1040 respondents rated themselves as above average drivers.

Would you like further details on this? Here are 5 related questions:

  1. What is the margin of error in surveys of this type?
  2. How do we interpret the claim that four-fifths of adults rate themselves as above average drivers?
  3. What is a confidence interval, and how could it apply here?
  4. How can sample size affect the accuracy of survey results?
  5. What statistical test can be used to compare the survey result with the claim?

Tip: Always round survey data logically, especially when dealing with real-world counts, like respondents.

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Math Problem Analysis

Mathematical Concepts

Percentage Calculation
Rounding
Statistical Survey Analysis

Formulas

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

Theorems

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Suitable Grade Level

Grades 9-12