Questions: Each of the following normal quantile plots illustrates a sample. In which cases is it reasonable to treat this as a sample from an approximately normal population? (More than one graph may be selected.)

Each of the following normal quantile plots illustrates a sample. In which cases is it reasonable to treat this as a sample from an approximately normal population? (More than one graph may be selected.)
Transcript text: Each of the following normal quantile plots illustrates a sample. In which cases is it reasonable to treat this as a sample from an approximately normal population? (More than one graph may be selected.)
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Solution

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Solution Steps

Step 1: Identify the purpose of the normal quantile plots

The purpose of normal quantile plots (Q-Q plots) is to determine if a data set is approximately normally distributed. If the points in the plot lie approximately along a straight line, the data can be considered to come from a normal distribution.

Step 2: Analyze each plot for linearity
  • Top-left plot: The points deviate significantly from a straight line, especially at the tails. This suggests the data is not normally distributed.
  • Top-right plot: The points lie approximately along a straight line, indicating the data is likely normally distributed.
  • Bottom-left plot: The points lie approximately along a straight line, indicating the data is likely normally distributed.
  • Bottom-right plot: The points lie approximately along a straight line, indicating the data is likely normally distributed.
Step 3: Determine which plots indicate normality

Based on the analysis:

  • Top-right plot: Reasonable to treat as a sample from an approximately normal population.
  • Bottom-left plot: Reasonable to treat as a sample from an approximately normal population.
  • Bottom-right plot: Reasonable to treat as a sample from an approximately normal population.

Final Answer

The plots that illustrate samples that can be reasonably treated as from an approximately normal population are:

  • Top-right plot
  • Bottom-left plot
  • Bottom-right plot
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