6. Normal Distribution and Continuous Random Variables
Standard Normal Distribution
1:41 minutesProblem 2.2.19d
Textbook Question
Interpreting Normal Quantile Plots Which of the following normal quantile plots appear to represent data from a population having a normal distribution? Explain.
Verified step by step guidance1
Step 1: Understand the purpose of a normal quantile plot. A normal quantile plot is used to assess whether a dataset follows a normal distribution. If the data is normally distributed, the points in the plot will approximately form a straight line.
Step 2: Observe the plot provided. The x-axis represents the data values (X Values), and the y-axis represents the corresponding z-scores (standardized values). The green line represents the expected linear relationship if the data is normally distributed.
Step 3: Analyze the alignment of the data points with the green line. If the points closely follow the green line with minimal deviation, this suggests the data is likely from a population with a normal distribution. Significant deviations or curvature would indicate non-normality.
Step 4: Note any patterns or deviations. In the provided plot, the points generally follow the green line, but there are slight deviations at the lower and upper ends. These deviations could indicate minor departures from normality, but overall, the data appears reasonably linear.
Step 5: Conclude based on the analysis. Since the majority of the points align well with the green line, the plot suggests that the data is likely from a population having a normal distribution, with minor deviations that may not significantly affect the overall normality.
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