Consider the following two normal curves Which has the...

Consider the following two normal curves Which has the smaller mean, and which has the smaller standard deviation? (A) Smaller mean, $a$; smaller standard deviation, $a$ (B) Smaller mean, $a$; smaller standard deviation, $b$ (C) Smaller mean, $b$; smaller standard deviation, $a$ (D) Smaller mean, $b$; smaller standard deviation, $b$ (E) Smaller mean, $a$; same standard deviation

Consider the following two normal curves Which has the smaller mean, and which has the smaller
standard deviation?
(A) Smaller mean, $a$; smaller standard deviation, $a$
(B) Smaller mean, $a$; smaller standard deviation, $b$
(C) Smaller mean, $b$; smaller standard deviation, $a$
(D) Smaller mean, $b$; smaller standard deviation, $b$
(E) Smaller mean, $a$; same standard deviation

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Key Concepts

Normal Distribution

A normal distribution is a continuous probability distribution that is symmetric about its mean. It is characterized by its bell-shaped curve, where most of the data points cluster around the mean and the probabilities for values further away from the mean taper off equally in both directions. This concept is fundamental in statistics for representing real-world data that are influenced by many small, random disturbances.

Mean

The mean is the central value or average of a dataset and in the context of a normal distribution, it defines the location of the peak or center of the bell curve. The mean indicates where most data points are concentrated, so a curve with a smaller mean is shifted to the left relative to one with a larger mean.

Standard Deviation

The standard deviation measures the spread or dispersion of a dataset around its mean. In a normal distribution, a smaller standard deviation corresponds to a steeper and narrower bell curve, indicating that the data points are closely clustered around the mean. In contrast, a larger standard deviation results in a flatter and wider distribution, reflecting more variability in the data.

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