Question

One graph in the following figure represents a normal distribution with mean $\mu=10$ and standard deviation $\sigma=3$ The other graph represents a normal distribution with mean $\mu=10$ and standard deviation $\sigma=2 .$ Determine which graph is which and explain how you know. (GRAPH CANNOT COPY)

Name: Problem 23, Chapter 7: Fundamentals of Statistics
Uploaded: 2021-06-25T20:20:20-08:00
Duration: 1 min 8 s
Channel: Barsha Rana
Description: One graph in the following figure represents a normal distribution with mean μ=10 and standard deviation σ=3 The other graph represents a normal distribution with mean μ=10 and standard deviation σ=2 . Determine which graph is which and explain how you know. (GRAPH CANNOT COPY)

   One graph in the following figure represents a normal distribution with mean $\mu=10$ and standard deviation $\sigma=3$ The other graph represents a normal distribution with mean $\mu=10$ and standard deviation $\sigma=2 .$ Determine which graph is which and explain how you know. (GRAPH CANNOT COPY)

Fundamentals of Statistics

Michael Sullivan III 5th Edition

Chapter 7, Problem 23

Instant Answer

Solved by Expert Barsha Rana

06/25/2021

Step 1

The mean, denoted by $\mu$, is the center of the distribution. In this case, both distributions have the same mean of 10, so they are centered at the same point on the x-axis. Show more…

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One graph in the following figure represents a normal distribution with mean $\mu=10$ and standard deviation $\sigma=3$ The other graph represents a normal distribution with mean $\mu=10$ and standard deviation $\sigma=2 .$ Determine which graph is which and explain how you know. (GRAPH CANNOT COPY)

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Key Concepts

Mean

The mean is the central value of a distribution and indicates where the peak of the bell curve is located. In a normal distribution, the mean divides the data symmetrically and establishes the center point around which the distribution is balanced.

Standard Deviation

Standard deviation quantifies the amount of spread or dispersion in a distribution. A smaller standard deviation results in a steeper and narrower curve, indicating that the data points are closely clustered around the mean, while a larger standard deviation produces a flatter and wider curve, signifying that the data points are more spread out.

Normal Distribution

A normal distribution is a continuous probability distribution known for its bell-shaped curve and symmetry about the mean. It is fully described by its mean and standard deviation, which determine the center and the spread of the distribution.

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