Determine whether the graph shown could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation. This image features a line graph with a smooth, curved line plotted on a two-dimensional plane. - **Axes:** - The horizontal axis (x-axis) is labeled "x" and ranges from 21 to 45. - The vertical axis (y-axis) is not labeled, but it supports the graphical representation of the function.- **Graph Description:** - The graph shows a curve that starts near the horizontal axis at x = 21. - It gradually rises to a peak around x = 39, indicating the maximum value of the function within this range. - After reaching this peak, the curve declines, approaching the x-axis as it reaches x = 45.This graph could represent various phenomena depending on the context, such as statistical data, a probability distribution, or a mathematical function, demonstrating a rise and fall in values across the given range on the x-axis.

Normal distribution is a continuous distribution which has many real life applications. Normal curve is a bell shaped curve. A standard normal distribution is a normal distribution with mean 0 and standard deviation 1. For a normal distribution, mean, median and mode is equal.One of the important properties of a normal curve is that it is symmetric about its mean. It is clear that the given curve is not symmetric and it is a left skewed distribution. So the given graph does not represent a variable with normal distribution. For a left skewed distribution mode will be greater than median and median will be greater than mean.

Answered: Determine whether the graph shown could…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Determine whether the graph shown could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.

This image features a line graph with a smooth, curved line plotted on a two-dimensional plane.

- **Axes:**
- The horizontal axis (x-axis) is labeled "x" and ranges from 21 to 45.
- The vertical axis (y-axis) is not labeled, but it supports the graphical representation of the function.

- **Graph Description:**
- The graph shows a curve that starts near the horizontal axis at x = 21.
- It gradually rises to a peak around x = 39, indicating the maximum value of the function within this range.
- After reaching this peak, the curve declines, approaching the x-axis as it reaches x = 45.

This graph could represent various phenomena depending on the context, such as statistical data, a probability distribution, or a mathematical function, demonstrating a rise and fall in values across the given range on the x-axis.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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