Math Problem Statement

Is it reasonable to treat the following as a sample from an approximately normal population? Explain.

Is it reasonable to treat the following as a sample from an approximately normal population? Explain.

Solution

To determine whether the histogram represents a sample from an approximately normal population, we should consider the following characteristics of a normal distribution:

  1. Symmetry: A normal distribution is symmetric around the mean.
  2. Unimodal: It should have a single peak (mode) in the middle.
  3. Bell-shaped curve: The frequencies should decrease as you move away from the mean in both directions.

Analyzing the given histogram:

  • The histogram appears roughly symmetric, with the peak occurring between 6 and 8.
  • It gradually decreases in frequency as you move away from the center in both directions.
  • There are no obvious outliers, large skewness, or multiple modes.

Thus, the histogram meets the general characteristics of a normal distribution. Therefore, it is reasonable to treat this sample as coming from an approximately normal population. The appropriate choices would be "none of these features" and "can" in the dropdown selections.

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Here are five related questions for further exploration:

  1. What are some statistical tests used to verify normality in a dataset?
  2. How would the presence of outliers affect the assessment of normality?
  3. What are the implications of assuming normality in hypothesis testing?
  4. How does sample size affect the appearance of a histogram for normality assessment?
  5. What are other methods for visualizing data to assess normality, besides histograms?

Tip: When assessing normality, combining graphical methods (like histograms or Q-Q plots) with statistical tests (e.g., Shapiro-Wilk test) provides a more comprehensive evaluation.

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Math Problem Analysis

Mathematical Concepts

Statistics
Normal Distribution
Data Visualization

Formulas

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Theorems

Characteristics of Normal Distribution

Suitable Grade Level

Grades 11-12