One graph in the following figure represents a normal...

One graph in the following figure represents a normal distribution with mean $\mu=8$ and standard deviation $\sigma=2$ The other graph represents a normal distribution with mean $\mu=14$ and standard deviation $\sigma=2 .$ Determine which graph is which and explain how you know. (GRAPH CANNOT COPY)

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Key Concepts

Normal Distribution

A normal distribution is a probability distribution that is symmetric about its mean, depicting that data near the mean are more frequent in occurrence than data far from the mean. Its bell-shaped curve is defined by its mean and standard deviation, which determine the center and spread, respectively.

Mean

The mean of a normal distribution is the central value where the curve is highest. It determines the location of the distribution on the horizontal axis, so a distribution with a larger mean will shift to the right relative to one with a smaller mean.

Standard Deviation

The standard deviation measures the spread or dispersion of the data around the mean. In a normal distribution, a smaller standard deviation results in a narrower, sharper peak, while a larger standard deviation produces a wider, flatter curve.

Graph Interpretation

When comparing two normal distributions on a graph, the distribution with the lower mean will appear shifted to the left relative to one with a higher mean, assuming identical standard deviations. This concept is critical for identifying which graph corresponds to which set of parameters based on their horizontal positions.

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