Which graphic shows data that is normally distributed, with equal variance?

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The correct choice indicates that the plot of residuals varies around the 0 line, which is characteristic of normally distributed data. When residuals are well-behaved and exhibit a normal distribution, they will cluster around zero with a symmetrical spread, reflecting that the differences between observed and predicted values are balanced.

In a normal distribution, we expect the residuals to appear randomly scattered when plotted against predicted values or another variable, without a discernible pattern, and to encompass both positive and negative values equally. This alignment around the zero line signifies that there is no systematic bias in the predictions; they are equally likely to be above or below the actual values.

Other options indicate potential issues or different characteristics in the distribution. For instance, a bell curve does depict a normal distribution, but simply saying it reflects a bell curve doesn’t capture the essential detail about the variance and symmetry expected around the zero line. An expanding pattern left to right indicates changing variance—which suggests heteroscedasticity rather than equal variance. Similarly, consistent spread across the range does not achieve the goal of demonstrating normal distribution if that spread isn't centered around zero with equal likelihood of being above or below. These nuances are key in understanding the concept of residuals in quality-driven management analysis.

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