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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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